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Distance Formula

Find the dist...

Question

Find the distances between the following points.
(i) A(a, 0), B(0, a) (ii) P(–6, –3), Q(–1, 9) (iii) R(–3a, a), S(a, –2a)

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Solution

(i) A(a, 0), B(0, a)
$AB = \sqrt{{(0 - a)}^{2} + {(a - 0)}^{2}} = \sqrt{a^{2} + a^{2}} = \sqrt{2 a^{2}} = a \sqrt{2}$

(ii) P(–6, –3), Q(–1, 9)
$PQ = \sqrt{{(- 6 - (- 1))}^{2} + {(- 3 - 9)}^{2}} = \sqrt{25 + 144} = \sqrt{169} = 13$

(iii) R(–3a, a), S(a, –2a)
$RS = \sqrt{{(- 3 a - a)}^{2} + {(a - (- 2 a))}^{2}} = \sqrt{16 a^{2} + 9 a^{2}} = \sqrt{25 a^{2}} = 5 a$

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