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Exercise 13 B

Q. 1. Find the coordinates of the midpoints of the line joining

1. (5, 8), (3, 2)
2. (-4, 2), (6, -8)
3. (a, -b), (3a, 5b)
4. (-2, -4), (-2, -6)

Q. 2. Find the co-ordinates of the point which divides the line joining

1. (3, 2), (5, 4) in the ratio 3 : 2
2. (-4, 2), (6, -8) in the ratio 2 : 3
3. (-a, +b), (2a, 4b) in the ratio 2 : 1

Q. 3. Vertices of a triangle are (-2, 11), (-2, -5) and (10, -1). Find the co-ordinates of midpoints of their sides. Also find the co-ordinates of its centroid.

Q. 4. If the mid-point of the sides of a triangle are (-2, -5), (3, -2) and (3, -1); find its vertices.

Q. 5. The co-ordinates of A and B are (2, a) and (-2, a+4). The mid-point of AB is (0, 1). Find the value of a.

Q. 6. In what ratio is the line joining (2, 3) and (4, 6) is divided by x-axis.

Q. 7. In what ratio is the line joining (-2, 5) and (6, 4) is divided by y-axis.

Q. 8. The center O of a circle has the co-ordinates (4, 5) and one point on the circumference is (8, 10). Find the co-ordinates of the other and of the diameter of the circle through this point.

Q. 9. The line joining A(2, 3) and B(6, -6) meets the x-axis at P. Write down the y-co-ordinate of P. Hence find the ratio AP : PB

Q. 10. The line segment joining A(2, 3) and B(4, -5) is intersected by the x-axis at a point K. Write down the ordinate of the point. Hence find the ratio in which K divides AB.

Q. 11. Calculate the ratio in which the line segment joining (3, 4) and (-2, 1) is divided by the y-axis.

Q. 12. P divides the distance between A (-2, 1) and B (1, 4) in the ratio 2 : 1. Calculate the co-ordinates of the point P.

Q. 13. Prove that the points A (-5, 4), B (-1, -2) and C (5, 2) are the vertices of an isosceles right angled triangle. Find the co-ordinates of D, so that ABCD is a square.

Q. 14. A(2, 2), B(-2, 4) and C (2, 6) are the vertices of a triangle ABC. Prove that ABC is an isosceles triangle.

Q. 15. Find the co-ordinates of the centroid of a triangle whose vertices are A (-1, 3), B (1, -1) and C (5, 1).

Q. 16. The line segment joining A (-1, 5/3) and B (a, 5) is divided in the ratio 1 : 3 at P, the point where the line segment AB intersects y-axis. Calculate

1. The value of a
2. The co-ordinate of P.

Q. 17. Calculate the ratio in which the line joining. A (6, 5) and B (4, -3) is divided by the line y = 2.

Q. 18. A (10, 5), B (6, -3) and C (2, 1) are the vertices of a triangle ABC. L is the mid-point of AB and M is the mid-point of AC. Write down the co-ordinates of L and M. Show that LM = ½ BC.

Q. 19. Two vertices of a triangle are (2, 3), (1, 2) and the centroid is (-1, -2). Find the third vertex.