Show that the given points are collinear: (– 3, – 4), (7, 2) and … - Vidyadip

Question

Show that the given points are collinear: (– 3, – 4), (7, 2) and (12, 5)

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Answer

The vertices are $A(-3,-4), B(7,2)$ and $C(12,5)$

Slope of a line $=\frac{y_2-y_1}{x_2-x_1}$
Slope of $A B=\frac{2+4}{7+3}=\frac{6}{10}=\frac{3}{5}$

Slope of $B C=\frac{5-2}{12-7}=\frac{3}{5}$
Slope of $A B=$ Slope of $B C=\frac{3}{5}$
$\therefore$ The three points $A, B, C$ are collinear.

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