Question

The points $(k,3),(2,-4)$ and $(-k+1,-2)$ are collinear, find $k$.

• A. $-\frac{1}{3}$
• B. $-3$
• C. $-1$
• D. $3$

Answer 1

The correct option is A $-\frac{1}{3}$

When three points A, B and C are
collinear, slope of line joining any two points (say AB) $=$ slope of line
joining any other two points (say BC).
Slope of the line passing through points $(x_1,y_1)$ and $(x_2,y_2)$ $=$ $\frac{y_2-y_1}{x_2-x_1}$
Slope of the line passing through $(k,3)$ and $(2,-4)=$
Slope of line passing through $\left(\right(-k+1),-2)$ and $(2,-4)$

$\frac{-4-3}{2-k}=\frac{-4-(-2)}{2-(-k+1)}$
$\frac{-7}{2-k}=\frac{-2}{1+k}$

On cross multiplying and solving, we get k $=-\frac{1}{3}$