Q. 1. Show that the points A (a, a), B (-a, -a) and 
form an equilateral triangle.
Q. 2. If the distance of P (x, y) from A (6,3) and B (-3,6) are equal prove that 3x = y.
Q. 3. If P and Q are two points whose coordinates are (at2, 2at) and a/t2, -2a/t) respectively, and S is the points (a, 0). Show that 1/SP + 1/SQ is independent of t.
Q. 4. 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.
Q. 5. In what ratio does the point (-2, 3) divides the line segments joining the points ( -3 , 5 ) and ( 4 , -9).
Q. 6. Find the length of the median through B and the coordinates of the centroid of a triangle whose vertices are A ( -1 , 3) , B (1, -1) and C (5 , 1).
Q. 7. The centroid of a triangle is at (4,-5). If two of its vertices are (2,5) and (3,-1), find its third vertex.
Q. 8. If the point P(0,2) is equidistant from the points (3,k) and (k,5) then find the value of k.
Q. 9. If p is the point of intersection of lines 3x + 4y = 7 and 2x + 3y = 5.Find the ratio in which P is divided by the line joining (2,3) and (3,5).
Q. 10. If the points A(1,0), B(a, 3), C(2, b) and D(-2, 4) are the vertices of a parallelogram, find the values of a and b.
Q. 11. Prove analytically that the line segments joining the mid-points of two sides of a triangle ABC , whose vertices are 
, is equal to half of the third side.
Q. 12. The three vertices of a rhombus, taken in order, are (2,-1), (3, 4) and (-2, 3). Find the fourth Vertex.
Q. 13. The co-ordinates of two points P and Q are 
and 
respectively and of a point S is (a,0). Show that 
.
Q. 14. 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.
O. 15. Determine the ration in which the line 3x + y – 9 = 0 divides the segment joining the pt (1,3) and (2,7)
Q. 16. Prove that quadrilateral formed by joining following points is a parallelogram.
(2, 1), (8, 9), (-3, 11) and (-9, 3)
Q. 17. Find the value of x if the distance between the points 
and 
is 5.
Q. 18. If the mid points of sides of the triangle are (2,6), (6.4) and (4,2) find its vertices.
Q. 19. Determine the ratio in which the point P(m, 6) divides the join of A(-4, 3) and B(2, 8). Also find the value.
Q. 20. Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6, 2) are the vertices of a square.
Q. 21. Show that the points A(2, —2), B(14, 10), C(11,13) and D(-1,1) are the vertices of a rectangle.
Q. 22. Determine the ratio in which the point (-6, a) divides the join of A(-3, -1) and B(-8,9). Also find the value of.
Q. 23. 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.
Q. 24. 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
Q. 25. The coordinates of the mid-point of the line joining the points and are find the values of.
Q. 26. Find the ratio in which the line-segment joining the points (6, 4) and (1, -7) is divided by x-axis.
Q. 27. Find the value of m for which the points with coordinates (3, 5), ( m , 6) and are collinear.
Q. 28. Find the value of k for which the points with coordinates (3, 2), (4, k) and (5, 3) are collinear.
Q. 29. If the point P(x, y) is equidistant from the points A (5, 1) and B (-1, 5), prove that 3x - 2y = 0
Q. 30. 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.
Q. 31. Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1); (1, 3) and (x, 8) respectively.
