1. In what ratio, does x - axis divide the line segment joining the points A (3,6) and B (-12,-3)?

2. If (a, b) is the mid-point of the segment joining the points A (10, -6) and B (k, 4) and a - 2b = 18, the value of k is

3. The coordinates of the vertex A of a rectangle ABCD whose three vertices are given as B(0, 0), C (3, 0) and D(0, 4) are

4. The distance between the points P (- 11/3 ,5 ) and Q (- 2/3, 5)  is

5. If end points of a diameter of a circle are (-5, 4) and (1, 0), then the radius of the circle is

6.  The distance of the point (-6, 8) from x-axis is

7.  If A( 3, √3),  B(0, 0) and C (3, k) are the three vertices of an equilateral triangle ABC, then the value of k is

8. The coordinate of the point which is reflection of the point (-3, 5) in X-axis are

9. The distance between the points (a cos θ+ b sin θ, 0) and (0, a sin θ - b cos θ) is

10. AD is a median of ΔABC with vertices A (5, - 6), B (6, 4) and C (0, 0), length of  AD is

11. A (5, 1), B (1, 4) and C (8, 5) are the coordinates of the vertices of a triangle. Which of the following types of triangle will ∆ABC be?

12. Two concentric circles are centred at O(-4, 3). The ratio of the area of inner circle to that of the outer circle is 1:9. Points A and B lie on the boundaries of the inner and outer circle, respectively, as shown in Fig.

The coordinates of point B are (3,5). Which of the following are the coordinates of A?

13. What is the ratio in which the line segment joining (2, – 3) and (5, 6) is divided by x-axis ?

14. The ratio in which the line 3x + y - 9 = 0 divides the line segment joining the points (1, 3) and (2, 7) is

15. The fourth vertex D of a parallelogram ABCD whose three vertices are A (-2, 3) , B (6, 7) and C (8, 3) is

16. The distance between two points, M and N, on a graph is given as √10^2 + 7^2. The coordinates of point M are (-4, 3). Given that the point N lies in the first quadrant, which of the following is true about the all possible x coordinates of point N?

17.  A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?

18. PQ is a line segment such that the y coordinate of P is - 1 and Q lies on the y-axis. The mid point of PQ is       O (-3,- 6). The coordinates of Q are

19. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2,-5) is the midpoint of PQ, then the coordinates of P and Q are, respectively

20. The distance between the points (0, 2√5) and (-2√5, 0) is