Find the value of x for which the points (x, -1)(2, 1) and (4, 5)… - Vidyadip

Question

Find the value of x for which the points (x, -1)(2, 1) and (4, 5) are collinear.

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Answer

Let A(x, -1), B (2, 1) and C (4, 5) be three collinear points.
$\therefore$ Slope of AB $= \frac{{1 - ( - 1)}}{{2 - x}} = \frac{{1 + 1}}{{2 - x}} = \frac{2}{{2 - x}}$
Slope of BC = $\frac{{5 - 1}}{{4 - 2}} = \frac{4}{2} = 2$
Since points A,Band C are collinear therefore slope of AB=slope of BC
2/2-x=2
Hence x=2

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