Q. 1. The centre of the circle is (-1, 6) and one end of a diameter is (5, 9), find the coordinates of the other end.
Q. 2. If (3, 0), (2, a) and (b, 6) are the vertices of a triangle ABC whose centroid is (2, 5). Find the values of a and b.
Q. 3. If A(-1, 3), B(1, -1) and C(5, 1) are the three vertices of a triangle ABC, find the length of median through B.
Q. 4. If (3, 2), (4, 4) and (1, 3) are the mid-points of the sides of a triangle, find the coordinates of the vertices of the triangle.
Q. 5. Using section formula show that (4, -11), (5, 3), (2, 15) and (1, 1) are the vertices of a parallelogram.
Q. 6. In what ratio is the line segment joining the points (-2, -3) and (3, 7) divided by the y-axis? Also find the coordinates of the point of division.
Q. 7. Find the point which represents the three-fourths of the distance from (3, 2) to (-5, 6).
Q. 8. Find the coordinates of the centre of circle, the coordinates of the end points of whose diameters are (-5, -2) and (7, -6). Also find the radius of the circle.
Q. 9. In what ratio does the point (3, 12) divide the line segment joining the points (1, 4) and (4, 16) ?
Q. 10. Find the coordinates of the points of trisection of the line segment joining the points (4, -8) and (7, 4).
Q. 11. Find the coordinates of a point which divide the segment AB in the ratio 3:5 internally, where A and B are (4, -1) & (7, 4) respectively.
Q. 12. Find the coordinates of point on the line joining A(3, -4) and B(-2, 5) that is twice as far from A as from B.
Q. 13. The mid-point of the line segment joining (3p, 4) and (-2, 2q) is (2, 2p + 2). Find the values of p and q.
Q. 14. Find the coordinates of a point whose distance from (3, 5) is 5 units and that from (0, 1) is 10 units.
Q. 15. An equilateral triangle has one vertex at (3, 4) and another at (-2, 3). Find the coordinates of the third vertex.
