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Mathematics Question on Coordinate Geometry

Find the distance between the following pairs of points :
(i) (2, 3), (4, 1)
(ii) (– 5, 7), (– 1, 3)
(iii) (a, b), (– a, – b)

Answer

The distance between the two points is given by
(x1−x2)2+(y1−y2)2\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

(i) The distance between (2, 3), (4, 1) is given by

l=(2−4)2+(3−1)2l=\sqrt{(2-4)^2+(3-1)^2}
l=(−2)2+(2)2l=\sqrt{(-2)^2+(2)^2}
l=4+4l=\sqrt{4+4}
l=8l=\sqrt8
l=22l=2\sqrt2

(ii) distance between (– 5, 7), (– 1, 3) is given by

l=(−5−(−1))2+(7−3)2l=\sqrt{(-5-(-1))^2+(7-3)^2}
l=(−4)2+(4)2l=\sqrt{(-4)^2+(4)^2}
l=16+16l=\sqrt{16+16}
l=32l=\sqrt{32}
l=42l=4\sqrt2

(iii) distance between (a, b), (– a, – b) is given by

l=(a−(−a))2+(b−(−b))2l=\sqrt{(a-(-a))^2+(b-(-b))^2}
l=(2a)2+(2b)2l=\sqrt{(2a)^2+(2b)^2}
l=4a2+4b2l=\sqrt{4a^2+4b^2}
l=2a2+b2l=2\sqrt{a^2+b^2}