Answer
Collinear.
Work Step by Step
Three points are collinear if the sum of the
distances between two pairs of the points is equal to the distance between the remaining pair of points
The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is:
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}~~~(1)$
Given :
$P(-4,3) ,Q(2,5) ,R(-1,4)$
we use formula (1) to calculate the distances between the given points:
$d_{PQ}=\sqrt{(-2-(-4))^2+(5-3)^2}=\sqrt{40}=2\sqrt{10}$
$d_{QR}=\sqrt{(-1-2)^2+(4-5)^2}=\sqrt{10}$
$d_{RP}=\sqrt{(-4-(-1))^2+(3-4)^2}=\sqrt{10}$
Because $\sqrt{10}+\sqrt{10}=2\sqrt{10}$, it follows that
$d_{QR}+d_{RP}=d_{PQ}$,
so the three points are collinear.
