1.   Find the distance between the following pairs of points :

(i)  (2, 3), (4, 1)            (ii)  (– 5, 7), (– 1, 3)            (iii)  (a, b), (– a, – b)

2.   Find the distance between the points A(0, 0) and B(36, 15). Can you now find the distance between 
the two towns A and B .

3.   Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

4.   Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

6.   Name the type of quadrilateral formed, if any, by the following points,  and  give  reasons  for your answer:

(i)   (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0) (ii)   (–3, 5), (3, 1), (0, 3), (–1, – 4) 
(iii)   (4, 5), (7, 6), (4, 3), (1, 2)

7.   Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

8.   Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units. 

9.   If Q(0, 1) is equidistant from P(5, –3) and R(x, 6), find the values of x. Also find the distances QR and PR.

10.   Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (– 3, 4).

Solution