SELF TEST:
1. The centre of a circle is (2a, a – 7). Find the values of a, if the circle passes through the point (11, –9) and has a diameter 10√ 2 units.( 3 marks)
2. Find the ratio in which the line 2x + 3y – 5 = 0 divides the line segment joining the points (8, –9) and (2, 1). Also, find the coordinates of the point of division.( 3 marks)
3. Show that the points (1, 7), (4, 2), (–1, –1) and (– 4, 4) are the vertices of a square.( 3 marks)
4. Find the point on the x-axis, which is equidistant from (2, –5) and (–2, 9).( 2 marks)
5. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order. [Hint: Area of a rhombus = 1/2 (product of its diagonals)]( 3 marks)
6. If the points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram, find the value of a and height of the parallelogram taking AB as the base.( 3 marks)