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Question
Determine whether the given set of points are collinear or not
(a, −2), (a, 3), (a, 0)
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Solution
A(a, −2), B(a, 3), C(a, 0)
Distance AB = `sqrt(("a" - "a")^2 + (3 + 2)^2`
= `sqrt(0 + 5^2)`
= `sqrt(25)`
= 5
BC = `sqrt(("a" - "a")^2 + (0 - 3)^2`
= `sqrt(0 + 9)`
= `sqrt(9)`
= 3
AC = `sqrt(("a" - "a")^2 + (0 + 2)^2`
= `sqrt(0 + 2^2)`
= `sqrt(4)`
= 2
AC + BC = AB
⇒ 2 + 3 = 5
∴ The given three points are collinear.
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