Question

The foot of the perpendicular from the point $(2, 4)$ upon $x + y = 4$ is

• A. $(3,-1)$
• B. $(2,2)$
• C. $(4,0)$
• D. $(1,3)$

Answer 1

Answer: (D)

$(1,3)$

Answer 2

The equation of line perpendicular to $x+y=4$ is $y-x=\lambda$. Also, it passes through $(2,4)$. $\therefore \,\,\,\,4-2=\lambda$ $\Rightarrow\,\,\,\, \lambda=2$ $\therefore\,\,\,$ Perpendicular line is $y-x=2$ The point of intersection of these lines are $(1,3)$.