Let us calculate the distances between the two points given below:

(i) (5, 7) and (8, 3)

(ii) (7, 0) and (2, –12)

(iii) and (0, –2)

(iv) (3, 6) and (–2, –6)

(v) (1, –3) and (8, 3)

(vi) (5, 7) and (8, 3)

Let us calculate the distances of the following points from origin:

(i) (7, –24)

(ii) (3, –4)

(iii) (a + b, a – b)

Let us prove that the point (–2, –11) is equidistant from the two points (–3, 7) and (4, 6).

Let us show that the points (7, 9), (3, –7) and (–3, 3) are the vertices of a right angled triangle by calculation.

Let us prove that in both of the following cases, the three points are the vertices of an isosceles triangle:

(i) (1, 4), (4, 1) and (8, 8)

(ii) (–2, –2), (2, 2) and (4, –4)