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COORDINATE GEOMETRY

 

Sample Paper – 2009

Class – X

Subject – Mathematics

 

COORDINATE GEOMETRY- ASSIGNMENT

  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.

 


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