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Question
Find distance CD where C(–3a, a), D(a, –2a).
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Solution
Let C(x1, y1) and D(x2, y2) be the given points.
∴ x1 = –3a, y1 = a, x2 = a, y2 = –2a
By distance formula,
d(C, D) = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
= `sqrt([a - (-3a)]^2 + (-2a - a)^2`
= `sqrt((a + 3a)^2 + (-2a - a)^2`
= `sqrt((4a)^2 + (-3a)^2`
= `sqrt(16a^2 + 9a^2)`
= `sqrt(25a^2)`
∴ d(C, D) = 5a units
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