Question

If $(1,2)$, $(\frac{1}{2},3)$ and $(0,k)$ are collinear points, find the value of $k$.

Answer 1

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 $(1,2)$ and $(\frac{1}{2},3)=$ Slope of line passing through $(\frac{1}{2},3)$ and $(0,k)$

$\frac{3-2}{\frac{1}{2}-1}=\frac{k-3}{0-\frac{1}{2}}$
$\frac{1}{-\frac{1}{2}}=\frac{k-3}{-\frac{1}{2}}$

On solving, $k=4$