Tiêu đề X - Maths - COORDINATE GEOMETRY.pdf ✅

1 CO-ORDINATE GEOMETRY EXERCISE – 1 (FOR SCHOOL/BOARD EXAMS) OBJECTIVE TYPE QUESTIONS CHOOSE THE CORRECT OPTION IN EACH OF THE FOLLOWING 1. The distance between the points (a, b) and (-a, - b) is : (A) 2 2 a b (B) 2 2 a b (C) 0 (D) 2 2 2 a b 2. The distance between points (a + b, b + c) and (a – b, c - b) is : (A) 2 2 2 a  b (B) 2 2 2 a  c (C) 2. 2b (D) 2 2 a  c 3. The distance between points A(1, 3) and B(x, 7) is 5. The value of x > 0 is : (A) 4 (B) 2 (C) 1 (D) 3. 4. The distance between the points (a cos 200 + b sin 200 ,0) and (a sin 200 - b cos 200 ) is : (A) (a + b) (B) (a – b) (C) 2 2 a  b (D) 2 2 a b 5. Mid-point of the line-segment joining the points (-5, 4) and (9, - 8) is : (A) (–7, 6) (B) (2, – 2) (C) (7, – 6) (D) (–2, 2). 6. The co-ordinates of the points which divides the join of (–2, 2) and (–5, 7) in the ratio 2 : 1 is : (A) (4, – 4) (B) (–3, 1) (C) (–4, 4) (D) (1, –3). 7. The co-ordinates of the points on x-axis which is equidistant from the points (5, 4) and (–2, 3) are : (A) (2, 0) (B) (3, 0) (C) (0, 2) (D) (0, 3). 8. The co-ordinates of the points on y-axis which is equidistant from the points (3, 1) and (1, 5) are : (A) (0, 4) (B) (0, 2) (C) (4, 0) (D) (2, 0). 9. The coordinates of the centre of a circle are (– 6, 1.5). If the ends of a diameter are (– 3, y) and (x, - 2) then: (A) x = - 9, y = 5 (B) x = 5, y = - 9 (C) x = 9, y = 5 (D) None of these 10. The points (- 2, 2), (8, - 2) and (-4, - 3) are the vertices of a : (A) equilateral  (B) isosceles  (C) right  (D) None of these 11. The points (1, 7), (4, 2) (- 1, 1) (- 4, 4) are the vertices of a : (A) parallelogram (B) rhombus (C) rectangle (D) square. 12. The line segment joining (2, - 3) and (5, 6) is divided by x-axis in the ratio: (A) 2 : 1 (B) 3 : 1 (C) 1 : 2 (D) 1 : 3. 13. The line segment joining the points (3, 5) and (- 4, 2) is divided by y-axis in the ratio: (A) 5 : 3 (B) 3 : 5 (C) 4 : 3 (D) 3 : 4.
2 14. If (3, 2), (4, k) and (5, 3) are collinear then k is equal to : (A) 3 2 (B) 5 2 (C) 2 5 (D) 5 3 15. If the points (p, 0), (0, q) and (1, 1) are collinear then p q 1 1  is equal to : (A) – 1 (B) 1 (C) 2 (D) 0 16. Two vertices of a triangle are (-2, -3) and (4, -1) and centroid is at the origin. The coordinates of the third vertex of the triangle are : (A) (– 2, 3) (B) (–3, – 2) (C) (–2, 4) (D) (4, –2) 17. A (5, 1), B(1, 5) and C(–3, –1) are the vertices of  ABC. The length of its median AD is : (A) 34 (B) 35 (C) 37 (D) 6 18. Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertex are : (A) (–3, 2) (B) (2,– 3) (C) (3, 2) (D) (– 2, –3) 19. The vertices of a parallelogram are (3, –2), (4, 0), (6,– 3) and (5,– 5). The diagonals intersect at the point M. The coordinates of the point M are : (A)       2 5 , 2 9 (B)       2 5 , 2 7 (C)       2 3 , 2 7 (D) None of these 20. If two vertices of a parallelogram are (3, 2) and (–1, 0) and the diagonals intersect at (2, –5), then the other two vertex are : (A) (1,– 10), (5, –12) (B) (1,– 12), (5, –10) (C) (2, – 10) (D) (1, – 10), (2, – 12) Que. 1 2 3 4 5 6 7 8 9 10 Ans. D C A C B C A B A C Que. 11 12 13 14 15 16 17 18 19 20 Ans. D A D C C C C C A B OBJECTIVE ANSWER KEY EXERCISE-4
3 EXERCISE – 1 (FOR SCHOOL/BOARD EXAMS) SUBJECTIVE TYPE QUESTIONS SHORT ANSWER TYPE QUESTIONS 1. Find the distance between the points A and B in the following : (i) A(a b,ba),B(a b,a b) (ii) ) 2 1 , 2 1 A(1,1),B( 2. Find the distance between the points A and B in the following : (i) A(82),B(36) (ii) A(a b,a b),B(a b,a b) 3. A point P lies on the x-axis and has abscissa 5 and a point Q lies on y-axis and has ordinate – 12. Find the distance PQ. 4. Find a relation between x and y such that the point (x, y) is equidistant from (7, 1) and (3, 5). 5. Using distance formula, show that the points A, B and C are collinear. (i) A(1,1),B(2,3),C(8,11) (ii) A(4,2),B(1,1),C(1, 3) 6. Find a point on the x-axis which is equidistant from the points (5, 4) and (-2, 3). 7. Find a point on the x-axis which is equidistant from the points (-3, 4) and (2, 3). 8. Find the value of k, if the point (2, 3) is equidistant from the points A(k, 1) and B(7, k). 9. Find the value of k for which the distance between the point A(3k, 4) and B(2, k) is 5 2 units. 10. Find the co-ordinates of the point which divides the line segment joining the points (1, -3) and (-3, 9) in the ratio 1 : 3 internally. 11. Find the mid-point of AB where A and B are the points (-5, 11) and (7, 3) respectively. 12. The mid-point of a line segment is (5, 8). If one end points is (3, 5), find the second end point. 13. The vertices of a triangle are A(3, 4), (7, 2) and C(-2, -5). Find the length of the median through the vertex A. 14. The co-ordinates of A and B are (1, 2) and (2, 3) respectively. Find the co-ordinates of R on line segment AB so that 3 4  RB AR . 15. Find the co-ordinates of the centre of a circle, the co-ordinates of the end points of a diameter being (-3, 8) and (5, 6) 16. Find the co-ordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and (1, 2) meet. 17. Find the ratio in which the line segment joining the points (3, 5) and (-4, 2) is divided by y-axis. 18. In what ratio in does the point        2 3 , 2 1 divide the line segment joining the points (3, 5) and (-7, 9) ? 19. By using section formula, show that the points (-1, 2), (2, 5) and (5, 8) are collinear. 20. Find the distance of the point (1, 2) from the mid-point of the line segment joining the points (6, 8) and (2, 4). 21. Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).
4 22. Find the area of the triangle whose vertices are (3, 2) (-2, -3) and (2, 3). 23. For what value of m, the points (3, 5), (m, 6) and       2 15 , 2 1 are collinear ? LONG ANSWER TYPE QUESTION 1. Prove that the points (1, 4), (3, 6) and (9, -2) are the vertices of an isosceles triangle. 2. Find the co-ordinates of the point equidistant from three given points A(5, 1), B(-3, -7) and C(7, -1). 3. Show that the points (7, 10), (-2, 5) and (3, - 4) are the vertices of an isosceles right triangle. 4. Prove that the points (0, 1), (1, 4), (4, 3) and (3, 0) are the vertices of a square. 5. Prove that the points (-4,- 1), (-2,- 4), (4, 0) and (2, 3) are the vertices of a rectangle. 6. If two vertices of an equilateral triangle are (0, 0) and (3, 3) , find the third vertex of the triangle. 7. A (3, 4) and C (1, -1) are the two opposite angular points of a square ABCD. Find the co-ordinates two vertices 8. Find the co-ordinates of the point equidistant from the point A(-2, -3), B(-1, 0) and C(7, -6). 9. Show that (3, 3) is the centre of the circle passing through the points (4, 6), (0, 4), (6, 2) and (4, 0). What radius of the circle. 10. If A (2, -1), B(3, 4), C(-2, 3) and D (-3, -2) be four points in a co-ordinates plane, show that ABCD is a rhombus but not a square. Find the area of the rhombus. 11. In figure, find the co-ordinates of the centre of the circle which is drawn through the points A, B and O.