Question

Find the value of $k$, if the points $A(7,-2),B(5,1)$ and $C(3,2k)$ are collinear.

Answer 1

$A(7,-2),B(5,1)andC(3,2k)$

Two points are said to be collinear if their slopes are equal

$\Rightarrow$ Slope of $AB$ $=$Slope of $BC$

We have,

Slope between two points$=\left(\frac{y_2-y_1}{x_2-x_1}\right)$

$\Rightarrow$ $\frac{1+2}{5-7}=\frac{2k-1}{3-5}$

$\Rightarrow$ $\frac{3}{-2}=\frac{2k-1}{-2}$

$\Rightarrow$ $-2(2k-1)=-6$

$\Rightarrow$ $2k-1=3$

$\Rightarrow$ $k=\frac{4}{2}$

$\Rightarrow$ $k=2$