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:

d = √[(x1 – x2)2 + (y1 – y2)2]

Distance between A(2, 3) and B(4, 1) is:

f =√ [(4 - 2)2 + (1 – 3)2]

= √[4 + 4]= √8

= 2√2

(ii) Distance between A(-5, 7) and B(-1, 3) is:

f = √[(-5 + 1)2 + (7 – 3)2]

= √[16 + 16] = √32

= 4√2

(iii) Distance between A(a, b) and B(-a, -b) is:

f = √[(a - (- a))2 + ( b - (-b))2]

f = √[(a+ a)2 + (b+ b)2]

f = √[2a + 2b] = √(4a2 + 4b2)

f = 2√(a2 + b2)

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