Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (– 5, 7), (– 1, 3)
(iii) (a, b), (– a, – b)
(i) We know that distance between the two points is given by:
= [(x1 – x2)2 + (y1 – y2)2]1/2
Distance between (2, 3) and (4, 1) is:
l = [(2 – 4)2 + (3 – 1)2]1/2
= [4 + 4]1/2 = (8)1/2
= 2
(ii) Distance between (-5, 7) and (-1, 3) is:
l = [(-5 + 1)2 + (7 – 3)2]1/2
= [16 + 16]1/2 = (32)1/2
= 4
(iii) Distance between (a, b) and (-a, -b) is:
l = [(a+ a)2 + (b+ b)2]1/2
= [2a + 2b]1/2 = (4a2 + 4b2)1/2
= 2
7