If the points $A(5, k), B(-3,1)$ and $C(-7,-2)$ are collinear, then $\mathrm{k}=$

If the points $A(5, k), B(-3,1)$ and $C(-7,-2)$ are collinear, then $\mathrm{k}=$
  1. $7$
  2. $\frac{-1}{7}$
  3. $\frac{1}{7}$
  4. $-7$

Solution

Slope of $A B=$ Slope of $B C$ $\begin{array}{l} \frac{1-k}{-3-5}=\frac{-2-1}{-7+3} \Rightarrow \frac{1-k}{-8}=\frac{-3}{-4} \\ \frac{1-k}{2}=-3 \Rightarrow k=7 \end{array}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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