1. Find the distance between the prints A (10 cos ?) and B (0, 10 sin ?)
2. Find the area of ABC where A (2, 3), B (-2, 1) and C (3, -2)
3. Find the co-ordinates of the point which divides the line-segment joining the point (1, 3) and (2, 7) in the ratio 3:4
4. Find the area of the triangle formed by the points O (0, 0), A (a, 0) and B (0, h).
5. AB is the diameter of a circle whose centre is (2, -3). If the co-ordinates of A.B are (1, 4), then find the co-ordinates of A.
6. Find the ratio in which the line-segment joining the points (-3, 4) and (1, -2) is divided by y-axis.
7. Find the point of trisection of the line-segment joining the points (-3, 4) and (1, -2).
8. In the figure BOA is a right triangle and C is the midpoint of AB. Show that it is equidistant from the vertices O, A and B.
9. If the area of a triangle formed by (x, 2x), (-2, 6) and (3, 1) is 5 square units, then find the value of x.
10. If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) at the origin, then find the value of a3 + b3 + c3.
11. The vertices of a ? ABC is (1, 2), (3, 1) and (2, 5). Point D divides AB in the ratio 2:1 and P is the mid-point of CD. Find the coordinates of the point P.
12. The line joining the points (2, 1) and (5, - 8) is trisected at the points P and Q. If the point P lies on the line 2x - y + k = 0, find the value of k
13. The area of a triangle is 5. Two of its vertices are (2, 1) and (3, -2). The third vertex lies on y = x + 3. Find the third vertex.
14. Find the value of k, if the point P (0, 2) is equidistant from (3, k) and (k, 5).
15. Find the distance between the points (a cos 350, 0) and ( 0, a cos 650)
16. Find the coordinate of the point at which the line 3x + 2y = 12 intersects the x -axis.
17. Find the ratio in which the line 2x + 3y - 30 = 0 divides the line segment joining the points ( 3, 4 ) and ( 7, 8). Find also the coordinates of the point of section.
18. Find the ratio in which the point P( m, 6 ) divides the join of A( - 4, 3 ) and B ( 2, 8 ). Also find the value of m.
19. Show that four point (2, -1); (3, 4); (-2,3) and (-3,-2) are vertices of a rhombus.
20. Find the roots of the equation 2x2 - 5 x + 3 =0 by the method of completing square.
21. Find the area of the quadrilateral whose vertices taken in order are (-4,-2); (-3,-5); (3,-2) and (2, 3).
22. Find the coordinates of the points of trisection of the line segment joining (4,-1) and (-2,-3).
23. The coordinates of the vertices of ?ABC are A(4, 1), B(3, 2) and C(0, K) Given that the area of ABC is 12 unit2, find the value of K
24. If two opposite vertices of a square are (5, 4) and (1, -6), find the coordinates of its remaining two vertices
25. If two vertices of an equilateral triangle be (0, 0), (3, v3), find the third side
26. Find the coordinates of a point P on y-axis equidistant from two points A (-3, 4) and B (3, 6) on the same plane.
27. Find the value of K for which the points A (-5, 1); B (1, K); and C (4,-2) are collinear. Also, find the ratio in which B divides AC.
28. Find the ratio in which the line joining the point (2,-6) and (8, 4) is divided by x-axis. Find the coordinate of the point of division.
29. Prove that the points A (-4,-1); B (-2,-4); C (5,-6) and D (2, 3) are the vertices of a rectangle.
30. Find the coordinate of the points which divide the line segment joining the points (-2, 0) and (0,8) in four equal parts.
31. Find the point which divides the line segment joining the points (-3,-4) and (-8, 7) in the ratio of 7:5.
32. In what ratio the line x-y-2=0 divides the line segment joining the points (3,-1) and (8,9). Find, also the coordinate of the point of intersection.
33. Find the coordinate of the points of trisection of the line segment joining the points (-1, 3) and (2, 5).
34. The vertices of a triangle are (3, 4); (7, 2); (-2,-3). Find the length of the median through the vertex A.
35. Find the area of a triangle whose vertices are (1,-1); (-4, 6) and (-3,-5).
36. Find the value of K, if the points (2, 3); (4, K) and (6, 3) are collinear.
37. Find the area of triangle whose vertices are (1, 2); (5, 3) and (18, 6).
38. Find the whether the points (4, 3); (5, 1) and (1, 9).
39. Prove that the (10, -18); (3, 6) and (-5, 2) are the vertices of isosceles.
40. Find the point on the y-axis which is equidistant from (-5, -2) and (3, 2).
41. Find the value of K, if the point P (0, 2) is equidistant from (3, K) and (K, 5).
42. Find the coordinates of a point which divides internally the line-segment joining the points (-3,-4) and (-8, 7) in the ratio 7:5
43. Find the ratio in which the line-segment joining the points (6, 4) and (1, -7) is divided internally by x-axis.
44. Find the coordinates of the points which divide the line-segment joining the points (-4, 0) and (0, 6) in four equal parts.
