Question

The coordinates of the foot of perpendicular drawn from the point $(2,4)$ on the line $x+y=1$, are

• A. $(\frac{1}{2},\frac{3}{2})$
• B. $(-\frac{1}{2},\frac{3}{2})$
• C. $(\frac{3}{2},-\frac{1}{2})$
• D. $(-\frac{1}{2},-\frac{3}{2})$

Answer 1

The correct option is B $(-\frac{1}{2},\frac{3}{2})$

Equation of line $\perp (x+y=1)$ and passing through $(2,4)$ will be
$y-4=(x-2)$
$\Rightarrow x-y+2=0\cdots \left(1\right)$
So intersection of $\left(1\right)$ with the given line will be foot of perpendicular of $(2,4)$
Hence foot of perpendicular will be $(-\frac{1}{2},\frac{3}{2})$