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ICSE Solutions for Class 10 Mathematics – Compound Interest

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Get ICSE Solutions for Class 10 Mathematics Chapter 1 Compound Interest for ICSE Board Examinations on APlusTopper.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

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Formulae

Formulae Based Questions

Question 1. Find the Compound Interest on Rs. 2,000 for 3 years at 15% per annum Compounded annually.

Question 2. If the interest is compounded half yearly, calculate the amount when the Principal is Rs. 7,400, the rate of interest is 5% per annum and the duration is one year.

Question 3. In how many years will Rs. 15,625 amount to Rs. 17,576 at 4% p.a., compound interest?

Question 4. The population of a city is 1,25,000. If the annual birth rate and death rate are 5.5% and 3.5% respectively. Calculate the population of the city after 3 years.

Question 5. There is a continuous growth in population of a village at the rate of 5% per annum. If its present population is 9,261, what population was 3 years ago?

Question 6. The population of a town 2 years ago was 62,500. Due to migration to cities, it decreases at the rate of 4% per annum. Find its present population.

Question. 7. The total number of industries in a particular portion of the country is approximately 1,600. If the government has decided to increase the number of industries in the area by 20% every year; find the approximate number of industries after 2 years.

Question 8. The cost of a machine depreciates by 10% every year. If its present worth is Rs.18,000; what will be its value after three years?

Question 9. 6000 workers were employed to construct a river bridge in four years. At the end of first year, 20% workers were retrenched; At the end of second year 5% of the workers at that time were retrenched. However, to complete the project in time, the number of workers was increased by 15% at the end of third year. How many workers were working during the fourth year?

Concept Based Questions

Question 1. The S.I. and C.I. on a sum of money for 2 years is Rs. 200 and 210 respectively. If the rate of interest is the same. Find the sum and rate.

Question 2. Find the difference between the simple interest and compound interest on 2,500 for 2 years at 4% p.a., compound interest being reckoned semi-annualy.

Question 3. A sum of money is lent out at compound interest for two years at 20% p.a., being reckoned yearly. If the same sum of the money was lent Gut at compound interest of the same rate of percent per annum C.I., being reckoned half yearly would have fetched Rs. 482 more by way of interest. Calculate the sum of money lent out.

Question 5. Mr. Kumar borrowed Rs. 15,000 for two years. The rate of interest for the two successive years are 8% and 10% respectively. If he repays Rs. 6,200 at the end of the first year, find the outstanding amount at the end of the second year.

Question 6. The compound interest, calculated yearly, on a certain sum of money for the second year is Rs. 1320 and for the third year is Rs. 1452. Calculate the rate of interest and the original sum of money.

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ICSE Solutions for Class 10 Mathematics – Circle Constructions

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Get ICSE Solutions for Class 10 Mathematics Chapter 16 Constructions (Circle) for ICSE Board Examinations on APlusTopper.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

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Figure Based Questions

Question 1. Take a point O on the plane at the paper. With O as centre draw a circle of radius 3 cm. Take a point P on this circle and draw a tangent at P.
Solution: Steps of construction:
(i) Take a point O on the plane at the paper and draw a circle at radius 3 cm.

Question 2. Four equal circles, each of radius 5 cm, touch each other as shown in the figure. Find the area included between them. (Take π= 3.14)

Question 3. In the figure alongside, OAB is a quadrant of a circle. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded 22 portion.

Question 4. AC and BD are two perpendicular diameter of a circle ABCD. Given that the area of shaded portion is 308 cm² calculate:

Question 5. The diagram represents the area swept by wiper of a car. With the dimension given in figure, calculate the shaded swept by the wiper.

Question 6. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take π = 3.14).

Question 7. Draw a circle at radius 4 cm. Take a point on it. Without using the centre at the circle, draw a tangent to the circle at point P.

Question 8. Draw a circle at radius 3 cm. Take a point at 5.5 cm from the centre at the circle. From point P, draw two tangent to the circle.

Question 9. Use a ruler and a pair of compasses to construct ΔABC in which BC = 4.2 cm, ∠ ABC = 60° and AB 5 cm. Construct a circle of radius 2 cm to touch both the arms of ∠ ABC of Δ ABC.

Question 10. Construct an isosceles triangle ABC such that AB = 6 cm, BC = AC = 4 cm. Bisect ∠C internally and mark a point P on this bisector such that CP = 5 cm. Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.

Question 11. Draw two lines AB, AC so that ∠ B AC = 40°:
(i) Construct the locus of the centre of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose centre lies within the ∠BAC.

Question 12. Draw a circle of radius 3.5 cm. Mark a point P outside the circle at a distance of 6 cm from the centre. Construct two tangents from P to the given circle. Measure and write down the length of one tangent.

Question 13. Construct a triangle ABC, given that the radius of the circumcircle of triangle ABC is 3.5 cm, ∠ BCA = 45° and ∠ BAC = 60°.
Solution: Steps of construction:

Question 14. Construct an angle PQR = 45°. Mark a point S on QR such that QS = 4.5 cm. Construct a circle to touch PQ at Q and also to pass through S.

Question 15. Construct the circumcircle of the ABC when BC = 6 cm, B = 55° and C = 70°.

Question 16. Using ruler and compass only, construct a triangle ABC such that AB = 5 cm, ABC = 75° and the radius of the circumcircle of triangle ABC is 3.5 cm.
On the same diagram, construct a circle, touching AB at its middle point and also touching the side AC.

Question 17. (a) Only ruler and compass may be used in this question. All contraction lines and arcs must be clearly shown and be of sufficient length and clarity to permit assessment.
(i) Construct a ABC, such that AB = AC = 7 cm and BC = 5 cm.
(ii) Construct AD, the perpendicular bisector of BC.
(iii) Draw a circle with centre A and radius 3 cm. Let this drcle cut AD at P.
(iv) Construct another circle, to touch the circle with centre A, externally at P, and pass through B and C.

Question 18. Using ruler and compass construct a cyclic quadrilateral ABCD in which AC = 4 cm, ∠ ABC = 60°, AB 1.5 cm and AD = 2 cm. Also write the steps of construction.

Question 19. Construct a triangle whose sides are 4.4 cm, 5.2 cm and 7.1 cm. Construct its circumcircle. Write also the steps of construction.
Solution: Steps of construction:

Question 20. Draw a circle of radius 3 cm. Construct a square about the circle.

Question 21. Draw a circle of radius 2.5 cm and circumscribe a regular hexagon about it.

Question 22. Construct the rhombus ABCD whose diagonals AC and BD are of lengths 8 cm and 6 cm respectively. Construct the inscribed circle of the rhombus. Measure its radius.

Question 23. Draw an isosceles triangle with sides 6 cm, 4 cm and 6 cm. Construct the in circle of the triangle. Also write the steps of construction.

Question 24. Use ruler and compasses only for this question:
(i) Construct A ABC, where AB = 3.5 cm, BC = 6 cm and ∠ ABC = 60°.
(ii) Construct the locus of points inside the triangle which are equidistant from BA and BC.
(iii) Construct the locus of points inside the triangle which are equidistant from B and C.
(iv) Mark the point P which is equidistant from AB, BC and also equidistant from B and C. Measure and record the length of PB.

Question 25. Construct a Δ ABC with BC = 6.5 cm, AB = 5.5 cm, AC = 5 cm. Construct the incircle of the triangle. Measure and record the radius of the incircle.

Question 26. Draw a circle of radius 4 cm. Take a point P out side the circle without using the centre at the circle. Draw two tangent to the circle from point P.
Solution: Steps of construction:
(i) Draw a circle of radius 4 cm.

Question 28. Ruler and compasses only may be used in this question. All constructions lines and arcs must be clearly shown, and the be sufficient length and clarity to permit assessment:
(i) Construct a triangle ABC, in which AB = 9 cm, BC = 10 cm and angle ABC = 45°.
(ii) Draw a circle, with centre A and radius 2.5 cm. Let it meet AB at D.
(iii) Construct a circle to touch the circle with center A externally at D and also to touch the line BC.

Question 30. The centre O of a circle of a radius 1.3 cm is at a distance of 3.8 cm from a given straight line AB. Draw a circle to touch the given straight line AB at a point P so that OP = 4.7 cm and to touch the given circle externally.

Question 31. Construct a triangle having base 6 cm, vertical angle 60° and median through the vertex is 4 cm.

Question 32. Using a ruler and compasses only:
(i) Construct a triangle ABC with the following data:
AB = 3.5 cm, BC = 6 cm and ∠ ABC = 120°.
(ii) In the same diagram, draw a circle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.
(iii) Measure ∠ BCP.

Question 33. Draw a circle of radius 3 cm and construct a tangent to it from an external point without using the centre.

Question 34. Construct a ΔABC with base BC = 3.5 cm, vertical angle ∠BAC = 45° and median through the vertex A is 3.5 cm. Write also the steps of construction.

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ICSE Solutions for Class 10 Mathematics – Circles

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Get ICSE Solutions for Class 10 Mathematics Chapter 15 Circles for ICSE Board Examinations on APlusTopper.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

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Formulae

Theorems based on chord properties:

1. Theorem: A straight line drawn from the centre of the circle to bisect a chord, which is not a diameter, is at right angles to the chord.
   Conversely, the perpendicular to a chord, from the centre of the circle, bisects the chord.
2. Theorem: There is one circle, and only one, which passes through three given points not in a straight line.
3. Theorem: Equal chords of a circle are equidistant from the centre.
   Conversely, chords of a circle, equidistant from the centre of the circle, are equal.
   

Theorems based on Arc and Chord properties:

1. Theorem: The angle which an arc of a circle subtends at the centre is double, that which it subtends at any point on the remaining part of the circumference.
2. Theorem: Angles in the same segment of a circle are equal.
3. Theorem: The angle in a semicircle is a right angle.
4. Theorem: In equal circles (or, in the same circle), if two arcs subtends equal angles at the centre, they are equal.
   Conversely, in equal circles (or, in the same circle), if two arcs are equal, they subtend equal angles at the centre.
5. Theorem: In equal circles (or, in the same circle), if two chord are equal, they cut off equal arcs.
   Conversely, in equal circles (or, in the same circle, if two arcs are equal the chords of the arcs are also equal.

Theorems based on Cyclic properties: ABCD is a cyclic quadrilateral.

1. Theorem: The opposite angles of a cyclic quadrilateral (quadrilateral inscribed in a circle) are supplementary.
2. Theorem: The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

Theorems based on Tangent Properties:

1. Theorem: The tangent at any point of a circle and the radius through this point are perpendicular to each other.
2. Theorem: If two circles touch each other, the point of contact lies on the straight line through the centres.
3. Theorem: From any point outside a circle two tangents can be drawn and they are equal in length.
4. Theorem: If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
5. Theorem: If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

Prove the Following 

Question 1. If a diameter of a circle bisect each of the two chords of a circle, prove that the chords are parallel.

Question 2. If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.

Question 3. In the given figure, OD is perpendicular to the chord AB of a circle whose centre is O. If BC is a diameter, show that CA = 2 OD.

Question 4. In Fig., l is a line intersecting the two concentric circles, whose common centre is O, at the points A, B, C and D. Show that AB = CD.

Question 6. ABCD is a cyclic quadrilateral AB and DC are produced to meet in E. Prove that

Question 7. In an isosceles triangle ABC with AB = AC, a circle passing through B and C intersects the sides. AB, and AC at D and E respectively. Prove that DE || BC.

Question 8. ABCD is quadrilateral inscribed in circle, having ∠A = 60°, O is the centre of the circle, show that

Question 9. Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA = QB

Question 11. Two circles are drawn with sides AB, AC of a triangle ABC as diameters. The circles intersect at a point D. Prove that D lies on BC.

Question 12. In the given figure, PT touches a circle with centre O at R. Diameter SQ when

Question 14. Prove that the line segment joining the midpoints of two equal chords of a circle substends equal angles with the chord.

Question 15. In an equilateral triangle, prove that the centroid and centre of the circum-circle (circumcentre) coincide.


Question 16. In Fig. AB and CD are two chords of a circle intersecting each other at P such that AP = CP. Show that AB = CD.

Question 17. Prove that the angle bisectors of the angles formed by producing opposite sides of a cyclic quadrilateral (Provided they are not parallel) intersect at right angle.

Question 18. In Fig. P is any point on the chord BC of a circle such that AB = AP. Prove that CP = CQ.

Question 19. The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from the point of their intersection on any side when produced backward bisects the opposite side.

Question 20. In a circle with centre O, chords AB and CD intersect inside the circumference at E. Prove that ∠AOC + ∠BOD = 2∠AEC.

Question 21. In Fig. ABC is a triangle in which ∠BAC = 30°. Show that BC is the radius of the circum circle of A ABC, whose centre is O.

Question 22. Prove that the circle drawn on any one of the equal sides of an isosceles triangles as diameter bisects the base.

Question 23. In Fig. ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD and BC in the points E and F respectively. Prove that EF || DC.

Question 25. If PA and PB are two tangent drawn from a point P to a circle with centre C touching it A and B, prove that CP is the perpendicular bisector of AB.

Question 26. Two circle with radii r₁ and r₂ touch each other externally. Let r be the radius of a circle which touches these two circle as well as a common tangent to the two circles, Prove that:

Question 27. If AB and CD are two chords which when produced meet at P and if AP = CP, show that AB = CD.

Question 28. In the figure, PM is a tangent to the circle and PA = AM. Prove that:

Question 29. In Fig. the incircle of ΔABC, touches the sides BC, CA and AB at D, E respectively. Show that:

Question 30. In Fig. TA is a tangent to a circle from the point T and TBC is a secant to the circle. If AD is the bisector of ∠BAC, prove that ΔADT is isosceles.

Question 32. In Fig. l and m are two parallel tangents at A and B. The tangent at C makes an intercept DE between n and m. Prove that ∠ DFE = 90⁰

Question 33. A circle touches the sides of a quadrilateral ABCD at P, Q, R, S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.

Question 34. Two equal chords AB and CD of a circle with centre O, when produced meet at a point E, as shown in Fig. Prove that BE = DE and AE = CE.

Question 35. Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral ABCD is also cyclic.

Figure Based Questions

Question 1. Two concentric circles with centre 0 have A, B, C, D as the points of intersection with the lines L shown in figure. If AD = 12 cm and BC s = 8 cm, find the lengths of AB, CD, AC and BD.

Question 2. In the given circle with diameter AB, find the value of x.

Question 3. In the given figure, the area enclosed between the two concentric circles is 770 cm². If the radius of outer circle is 21 cm, calculate the radius of the inner circle.

Question 4. Two chords AB and CD of a circle are parallel and a line L is the perpendicular bisector of AB. Show that L bisects CD.

Question 5. In the adjoining figure, AB is the diameter of the circle with centre O. If ∠BCD = 120°, calculate:

Question 6. Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

Question 7. The radius of a circle is 13 cm and the length of one of its chord is 10 cm. Find the distance of the chord from the centre.

Question 9. AB is a diameter of a circle with centre C = (- 2, 5). If A = (3, – 7). Find
(i) the length of radius AC
(ii) the coordinates of B.

Question 10. AB is a diameter of a circle with centre O and radius OD is perpendicular to AB. If C is any point on arc DB, find ∠ BAD and ∠ ACD.

Question 11. In the given below figure,

Question 14. In the given figure O is the centre of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm. Calculate the radius of the circle.

Question 15. In Fig., chords AB and CD of the circle intersect at O. AO = 5 cm, BO = 3 cm and CO = 2.5 cm. Determine the length of DO.

Question 16. In the figure given below, PT is a tangent to the circle. Find PT if AT = 16 cm and AB = 12 cm.

Question 18. A, B and C are three points on a circle. The tangent at C meets BN produced at T. Given that ∠ ATC = 36° and ∠ ACT = 48°, calculate the angle subtended by AB at the centre of the circle.

Question 19. In the given figure, O is the centre of the circle and ∠PBA = 45°. Calculate the value of ∠PQB.

Question 20. Two chords AB, CD of lengths 16 cm and 30 cm, are parallel. If the distance between AB and CD is 23 cm. Find the radius of the circle.

Question 21. Two circles of radii 10 cm and 8 cm intersect and the length of the common chord is 12 cm. Find the distance between their centres.

Question 22. AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm and AB || CD. If the distance between AB and CD is 3 cm, find the radius of the circle.

Question 24. AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm. If the chords are on the opposite sides of the centre and the distance between them is 17 cm, find the radius of the circle.

Question 26. In the figure given below,O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD.

Question 27. If O is the centre of the circle, find the value of x in each of the following figures

Question 29. In the given figure, AB is the diameter of a circle with centre O.

Question 30. In ABCD is a cyclic quadrilateral; O is the centre of the circle. If BOD = 160°, find the measure of BPD.

Question 32. In the given figure O is the centre of the circle, ∠ BAD = 75° and chord BC = chord CD. Find:

Question 37. ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.

Question 40. P and Q are the centre of circles of radius 9 cm and 2 cm respectively; PQ = 17 cm. R is the centre of circle of radius x cm, which touches the above circles externally, given that ∠ PRQ = 90°. Write an equation in x and solve it.

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ICSE Solutions for Class 10 Mathematics – Coordinate Geometry

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Get ICSE Solutions for Class 10 Mathematics Chapter 11 Coordinate Geometry for ICSE Board Examinations on APlusTopper.com. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

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Formulae

Formulae Based Questions

Question 1. Find the distance of the following points from origin.
(i) (5, 6)   (ii) (a+b, a-b)    (iii) (a cos θ, a sin θ).

Question 2. Calculate the distance between A (7, 3) and B on the x-axis, whose abscissa is 11.
Solution: Here B is (11, 0)

Question 3. KM is a straight line of 13 units If K has the coordinate (2, 5) and M has the coordinates (x, – 7) find the possible value of x.

Question 4. The midpoint of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a+1). Find the value of a and b.
show that the points A(- 1, 2), B(2, 5) and C(- 5, – 2) are collinear.

Question 5. Use distance formula to show that the points A(-1, 2), B(2, 5) and C(-5, -2) are collinear.

Determine the Following

Question 1. PQ is straight line of 13 units. If P has coordinate (2, 5) and Q has coordinate (x, – 7) find the possible values of x.

Question 2. Give the relation that must exist between x and y so that (x, y) is equidistant from (6, -1) and (2, 3).

Question 3. The line segment joining A (2, 3) and B (6, – 5) is intersected by the X axis at the point K. Write the ordinate of the point K. Hence find the ratio in which K divides AB.
Solution: A (2, 3) and B (6,- 5)

Question 4. Find the value of x so that the line passing through (3, 4) and (x, 5) makes an angle 135° with positive direction of X-axis.

Question 5. Find the value, of k, if the line represented by kx – 5y + 4 = 0 and 4x – 2y + 5 = 0 are perpendicular to each other.

Question 6. Find the equation of a line which is inclined to x axis at an angle of 60° and its y – intercept = 2.

Question 7. Find the equation of a line with slope 1 and cutting off an intercept of 5 units on Y-axis.
Solution: We have
Slope of the line m = 1

Question 8. Find the equations of a line passing through the point (2, 3) and having the x – interecpt of 4 units.

Question 9. The line through A (- 2, 3) and B (4, b) is perpendicular to the line 2a – 4y = 5. Find the value of b.

Question 11. Find the equation of a straight line which cuts an intercept of 5 units on Y-axis and is parallel to the line joining the points (3, – 2) and (1, 4).

Question 12. Find the equation of a line that has Y-intercept 3 units and is perpendicular to the line joining (2, – 3) and (4, 2).

Question 13. Find a general equation of a line which passes through:
(i) (0, -5) and (3, 0) (ii) (2, 3) and (-1, 2).

Question 14. Find the equation of the line passing through (0, 4) and parallel to the line 3x + 5y + 15 = 0.

Question 15. Find the equation of a line passing through (3, – 2) and perpendicular to the line.

Question 16. Find the equation of the straight line which has Y-intercept equal to 4/3 and is perpendicular to 3x – 4y + 11 = 0.

Question 17. Find the equation of the straight line perpendicular to 5x – 2y = 8 and which passes through the mid-point of the line segment joining (2, 3) and (4, 5).

Question 18. A line passing through the points (a, 2a) and (- 2, 3) is perpendicular to the line 4a + 3y + 5 = 0. Find the value of a.

Prove the Following 

Question 1. A line is of length 10 units and one end is at the point (2, – 3). If the abscissa of the other end be 10, prove that its ordinate must be 3 or – 9.

Question 2. Show that the line joining (2, – 3) and (- 5, 1) is:
(i) Parallel to line joining (7, -1) and (0, 3).
(ii) Perpendicular to the line joining (4, 5) and (0, -2).

Question 3. With out Pythagoras theorem, show that A(4, 4), B(3, 5) and C(-1, -1) are the vertices of a right angled.

Question 4. Show that the points A(- 2, 5), B(2, – 3) and C(0, 1) are collinear.

Question 5. By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).

Question 6. Show that each of the triangles whose vertices are given below are isosceles :
(i) (8, 2), (5,-3) and (0,0)
(ii) (0,6), (-5, 3) and (3,1).

Question 7. Show that the quadrilateral with vertices (3, 2), (0, 5), (- 3, 2) and (0, -1) is a square.

Question 9. If the point (x, y) is at equidistant from the point (a + b, b – a) and (a-b, a + b). Prove that ay = bx.

Question 10. Prove that A(4, 3), B(6, 4), C(5, 6) and D(3, 5) are the angular points of a square.

Question 14. Show that the points A(1, 3), B(2, 6), C(5, 7) and D(4, 4) are the vertices of a rhombus.

Figure Based Questions

Question 2. Determine the ratio in which the line 3x + y – 9 = 0 divides the line joining (1, 3) and (2, 7).

Question 3. The midpoint of the line segment AB shown in the diagram is (4, – 3). Write down the coordinates of A and B.
Solution: Let the coordinates of A and Bare (x, 0) and (0, y).

Question 4. The centre ‘O’ of a circle has the coordinates (4, 5) and one point on the circumference is (8, 10). Find the coordinates of the other end of the diameter of the circle through this point.

Hence (0, 0) be the coordinates of the other end.

Question 5. In the following figure line APB meets the X-axis at A, Y-axis at B. P is the point (4, -2) and AP : PB = 1 : 2. Write down the coordinates of A and B.

Question 6. The three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of the fourth vertex.

Question 7. Find the equation of a straight line which cuts an intercept – 2 units from Y-axis and being equally inclined to the axis.

Question 8. In ΔABC, A (3, 5), B (7, 8) and C (1, – 10). Find the equation of the median through A.

Question 10. In the adjoining figure, write

Question 11. In the figure given below, the line segment AB meets X-axis at A and Y-axis at B. The point P (- 3, 4) on AB divides it in the ratio 2 : 3. Find the coordinates of A and B.

Question 12. Determine the centre of the circle on which the points (1, 7), (7 – 1), and (8, 6) lie. What is the radius of the circle ?

Question 13. Find the image of a point (-1, 2) in the line joining (2, 1) and (- 3, 2).

Question 14. The line through P (5, 3) intersects Y axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the coordinates of Q.

Question 15. Find the value of ‘a’ for which the following points A (a, 3), B (2, 1) and C (5, a) are collinear. Hence find the equation of the line.

Question 16. If the image of the point (2,1) with respect to the line mirror be (5, 2). Find the equation of the mirror.

Question 17. The vertices of a triangle are A(10, 4), B(- 4, 9) and C(- 2, -1). Find the

Question 18. Given equation of line L₁ is y = 4.
(i) Write the slope of line, if L₂ is the bisector of angle O.
(ii) Write the coordinates of point P.
(iii) Find the equation of L₂

Question 19. From the adjacent figure:
(i) Write the coordinates of the points A, B, and

Graphical Depiction

Question 1. Given a line segment AB joining the points A (- 4, 6) and B (8, – 3). Find:
(i) the ratio in which AB is divided by the y- axis.
(ii) find the ordinates of the point of intersection.
(iii) the length of AB.

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