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Question
Determine whether the following point is collinear.
A(–4, 4), \[K\left( - 2, \frac{5}{2} \right),\] N (4, –2)
Solution
A(–4, 4), \[K\left( - 2, \frac{5}{2} \right),\] N (4, –2)
Slope of AK = `(5/2 - 4)/((-2) - (- 4))`
= `((5 - 8)/2)/((-2) + 4)`
= `((-3)/2)/2`
= `((-3)/2)/(2/1) = (-3)/2 xx 1/2 = (-3)/(2 xx 2)`
= `(-3)/4`
\[\text { Slope of KN } = \frac{(- 2) - \frac{5}{2}}{4 - \left( - 2 \right)}\]
= `(((-4) - 5)/2)/(4 + 2)`
= `((-9)/2)/(6/1) = (- 9)/2 xx 1/6 = (-9)/(6 xx 2) = (- 9)/12`
= `(- 3)/4`
Slope of AK = Slope of KN
Thus, the given points are collinear.
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