Question 1 (iii)
Find the distance between the following pairs of points:
(iii) (a, b), (− a, − b)

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Solution

(iii)Distance between the points is given by
$\sqrt{{(x_{1} - x_{2})}_{1}^{2} + {(y_{1} - y_{2})}_{1}^{2}}$
Therfore distance between (a, b) and (− a, − b) is given by
$l = \sqrt{{(a - (- a))}^{2} + {(b - (- b))}^{2}}$
$= \sqrt{{(2 a)}^{2} + {(2 b)}^{2}}$
$= \sqrt{4 a^{2} + 4 b^{2}} = 2 \sqrt{a^{2} + b^{2}}$

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