Question

Determine whether the following point is collinear.

A(–4, 4), \[K\left( - 2, \frac{5}{2} \right),\] N (4, –2)

Answer 1

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.