Question

If the points $(\frac{2}{5},\frac{1}{3}),(\frac{1}{2},k)$ and $(\frac{4}{5},0)$ are collinear then find the value of k

• A. $k=\frac{1}{2}$
• B. $k=\frac{1}{4}$
• C. $k=\frac{1}{5}$
• D. $k=-\frac{1}{2}$

Answer 1

The correct option is B $k=\frac{1}{4}$

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 $(\frac{2}{5},\frac{1}{3})$ and $(\frac{1}{2},k)=$ Slope of line passing through $(\frac{1}{2},k)$ and $(\frac{4}{5},0)$

$\frac{k-\frac{1}{3}}{\frac{1}{2}-\frac{2}{5}}=\frac{0-k}{\frac{4}{5}-\frac{1}{2}}$
On solving, $k=\frac{1}{4}$