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COORDINATE GEOMETERY

Sample Paper – 2010

Class – X
Subject – Mathematics

 

  1. The vertices of a triangle are A(3,4), B(7,2) and C(-2, -5).Find the length of the median through the vertex B.
  2. In what ration does the point (1/2, 6) divide the line segment joining the points  (3,5) and (-7,9).
  3. The co-ordinates of one end of the diameter of a circle are (3,5) and the co-ordinates of its center are (7,4). Find out the co-ordinates of the other end of the diameter.
  4. A is a point on the y-axis who’s ordinate is 5 and B is the point (3, 1). Calculate the length of AB
  5. The mid point of the line segment joining (2a, 4) and (2, 3b) is (1, 2a +1). Find the values of a and b.
  6. Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right-angled triangle. Also, prove that these are the vertices of an isosceles triangle.
  7. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by they-axis? Also, find the coordinates of the point of division.
  8. A (5, -1), B (-3, -2) and C (-1, 8) are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.
  9. Show that the points A (1, 2), B(S, 4), C(3, 8) and D(— 1,6) are the vertices of a square.
  10. Find the co-ordinates of the point equidistant from three given points A (5, 1), B (- 3, -7) and C (7, -1).
  11. Find the value of p for which the point (-1, 3), (2, p) and (5, -1) are collinear.
  12. If (-2, -1); (a, 0); (4, b) and (1, 2) are the vertices of a parallelogram, find the values of a and b.
  13. Prove that the points (-4, -1); (-2, -4); (4, 0) and (2, 3) are vertices of a rectangle.
  14. The vertices of a triangle are (—1, 3); (1, —1) and (5, 1). Find the lengths of medians through vertices (—1, 3) and (5, 1).
  15. By distance formula, show that the points (1, -1) (5, 2) and (9, 5) are collinear.
            1.  

 

  1. Show that the points A (2, -2), B (14, 10), C (11, 13) and D (-1, 1) are the vertices of a rectangle.
  2. Determine the ratio in which the points (6, a) divides the join of A (-3, -1) and B (-8, 9). Also find the value of “a”.
  3. Find the point on the x-axis which is equidistant from the points (-2, 5) and (2, -3).find the coordinates of a point which divides internally the line segment joining the points (-3,-4) and (-8, 7) in the ratio of 7:5.
  4. Find the value of k for which the points (2, 5), (k, 11/2) and (4, 6) are collinear.
  5. Find the lengths of the median of the triangle whose vertices are (1,-1), (0, 4) and (-5,3) .
  6. Find the co-ordinates of the points of trisection of the line segment joining the points (3, -3) and (6, 9).
  7. The center of a circle of radius 13 units is the point (3, 6). P (7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.
  8. The co-ordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.
  9. If ‘a’ is the length of one of the sides of an equilateral triangle ABC base BC lies on x-axis and vertex B is at the origin, find the coordinates of the vertices of the triangle ABC.
  10. The coordinates of the mid-point of the line joining the points (2p+1, 4) and (5, q – 1) are (2p, q). Find the value of p and q.
  11. Find the value of K for which the points with coordinates (3, 2), (4, K) and (5, 3) are collinear.
  12. A is a point on the y-axis whose ordinate is 5 and B is the point (-3, 1). Calculate the length of AB.
  13. The distance between A (1, 3) and B(x, 7) is 5. Find the possible values of x
  14. Show that the points (3, 3), (9, 0) and (12, 21) are the vertices of a right angled triangle.
  15. The center of a circle is (1, -2) and one end of a diameter is (-3, 2), find the co-ordinates of the other end.
  16. Find the area of the quadrilateral whose vertices , taken in order are (-6,-2), (-3,-5) ,(4,-2) and (2,4)
  17. Find area of the square whose points are A(5,6) B( 1,5) C(2,1)  D( 6,2).
  18. Determine the ratio in which the points P (m, 6) divides the join of A (-4, 3) and B (2, 8). Also find the value of m.
  19. Find the value of p for which the points (-1, 3), (2, p) and (5,-1) are collinear.
  20. Calculate the ratio in which the line joining A (6, 5) and B (4,-3) is divided by the line y=2. Also find the point of division.
  21. If the two opposite sides of the square are (5, 4) and (-1, 6). Find the other two.
  22. If the points (x,y) is equidistant from the points (2,1) and (1,-2). Show that x+3y=0.
  23. Show that the points (1, 1), (-1,-1) and ( form an isosceles triangle.Find the coordinates of third side of the triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3).Find area of triangle formed by (5, 6), (8, 9) and (2, 1).Show that the points (0, -1), (-2, 3), (6, 7) and (8, 3) are the vertices of a rectangle. The points A (0, 3), B (-2, a) and C (-1, 4) are the vertices of a right angled triangle at A, find the value of a. Find the value of k for which the points with coordinates (7, 5), (k, 11/2) and (2, 6) are collinear.

 

  1. Find the ratio in which the point (-3,p) divides the line segment joining the points (-5, -4) and (-2,3). Also find the value of p.(3)
  2. Determine the ration in which the line 3x + y – 9 = 0 divides the segment joining the pt (1,3) and (2,7).(3)
  3. Find the value of x if the distance between the points (x, 1) and (3,2) is 5. (3)
  4. If the mid points of sides of the triangle are (2,6), (6.4) and (4,2) find its vertices.(5)
  5. The coordinates of the mid-point of the line joining the points (3p, 4) and (-2, 2q) are (5, p). Find the values of p and q.
  6. Find the ratio in which the line-segment joining the points (6, 4) and (1, -7) is divided by x-axis.
  7. Find the value of m for which the points with coordinates (3, 5), (m, 6) and are collinear.
  8. Find the value of k for which the points with coordinates (3, 2), (4, k) and (5, 3) are collinear.
  9. If the point P(x, y) is equidistant from the points A (5, 1) and B (-1, 5), prove that 3x - 2y = 0(5)
  10. The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0, find the value of k.(5)
  11. The vertices of a triangle are A(3,4), B(7,2) and C(-2, -5).Find the length of the median through the vertex B.
  12. The co-ordinates of one end of the diameter of a circle are (3,5) and the co-ordinates of its center are (7,4). Find out the co-ordinates of the other end of the diameter
  13. Prove that the points (3, 0), (6, 4) and (-1, 3) are vertices of a right-angled triangle. Also, prove that these are the vertices of an isosceles triangle.
  14. If (-2, -1); (a, 0); (4, b) and (1, 2) are the vertices of a parallelogram, find the values of a and b.
  15. If the distance of P (x, y) from A (6,3) and B (-3,6) are equal prove that 3x = y.
  16. If the pt A(-2, -1) B(1, 0) C(x, 3) and D(1, y) lie on the ends of parallelogram find the value of X and y.
  17. Find the coordinates of point’s which trisect the line segment joining (1 , 2 ) and (-3 , 4 ).
  18. The area of a triangle is 5.Two of it’s vertices are (2,1) and (3, -2). The third vertex lies on y = x + 3.find the third vertex.(5)

 

 


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