Question

Find the value of k if A(−3, 11), B(6, 2) and C(k, 4) are collinear points.

Answer 1

Given: The points A(−3, 11), B(6, 2) and C(k, 4) are collinear.
∴ $$Slope of AB = slope of BC

$$\begin{gathered} \Rightarrow \frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_3} \\ \Rightarrow \frac{2-11}{6-(-3)}=\frac{4-2}{k-6} \\ \Rightarrow \frac{-9}{9}=\frac{2}{k-6} \\ \Rightarrow -1=\frac{2}{k-6} \\ \Rightarrow -k+6=2 \\ \Rightarrow -k=2-6 \\ \Rightarrow -k=-4 \\ \Rightarrow k=4 \end{gathered}$$