Question
Show that points $\mathrm{P}(-2,3), \mathrm{Q}(1,2), \mathrm{R}(4,1)$ are collinear.
✓
Answer
$\mathrm{P}(-2,3), \mathrm{Q}(1,2)$ and $\mathrm{R}(4,1)$ are given points
slope of line $\mathrm{PQ}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-3}{1-(-2)}=-\frac{1}{3}$
Slope of line $\mathrm{QR}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{4-1}=-\frac{1}{3}$
Slope of line PQ and line $\mathrm{QR}$ is equal.
But point $Q$ lies on both the lines.
$\therefore$ Point P, Q, R are collinear.
slope of line $\mathrm{PQ}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-3}{1-(-2)}=-\frac{1}{3}$
Slope of line $\mathrm{QR}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-2}{4-1}=-\frac{1}{3}$
Slope of line PQ and line $\mathrm{QR}$ is equal.
But point $Q$ lies on both the lines.
$\therefore$ Point P, Q, R are collinear.
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