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Question
Verify whether the following points are collinear or not:
A(1, –3), B(2, –5), C(–4, 7).
Solution
A ≡ (1, –3) ≡ (x1 ,y1),
B ≡ (2, –5) ≡ (x2, y2),
C ≡ (–4, 7) ≡ (x3, y3).
Slope of AB = ` (y_2 - y_1)/(x_2 - x_2)`
`=(-5 - (-3))/(2 - 1)`
`= (-5 + 3)/(2 - 1)`
= `(-2)/1`
= –2
Slope of BC = `(y_3 - y_2)/(x_3 - x_2)`
`= (7 - (-5))/(-4 - 2)`
= `(7 + 5)/(-4-2)`
`= 12/-6`
= –2
A, B, and C are collinear points that have B as a common point.
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