Question
The points $(K, 3), (2, −4)$ and $(-K + 1, −2)$ are collinear. Find K.
✓
Answer
Given, points $A (K, 3), B (2, −4)$ and $C (−K + 1, −2)$ are collinear.
$\therefore$ Slope of AB = Slope of BC
$\frac{-4-3}{2-k}=\frac{-2+4}{-k+1-2} $
$ \frac{-7}{2-k}=\frac{2}{-k-1} $
$7 k+7=4-2 k $
$9 k=-3 $
$k=\frac{-1}{3}$
$\therefore$ Slope of AB = Slope of BC
$\frac{-4-3}{2-k}=\frac{-2+4}{-k+1-2} $
$ \frac{-7}{2-k}=\frac{2}{-k-1} $
$7 k+7=4-2 k $
$9 k=-3 $
$k=\frac{-1}{3}$
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