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Question
Determine whether the sets of points are collinear?
`(-1/2, 3), (-5, 6) and (-8, 8)`
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Solution
Let the points be `"A"(-1/2, 3), "B" (-5, 6) and "C"(-8, 8)`
Area of ∆ABC = `1/2[(x_1y_2 + x_2y_3+ x_3y_1) - (x_2y_1 + x_3y_3 + x_1y_3)]`
= `1/2[(-3 - 40 - 24) - (-15 - 48 - 4)]`
=`1/2[-67 + 67]`
= `1/2 xx 0`
= 0
Area of a ∆ is 0.
∴ The three points are collinear.
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