Question

The coordinates of the foot of the perpendicular from the point (2, 3) on the line $x+y-11=0$ are

• A. (-6, 5)
• B. (5, 6)
• C. (-5, 6)
• D. (6, 5)

Answer 1

The correct option is B

(5, 6)

Let the coordinates of the foot of the perpendicular from the point (2, 3) on the line $x+y-11=0$ be (x, y)

Now, the slope of the line $x+y-11=0$ is -1

So, the slope of the perpendicular = 1 The equation of the perpendicular is given by

$y-3=1(x-2)$

$\Rightarrow x-y+1=0$

Solving $x+y-11=0$ and $x-y+1=0,$ we get

$x=5$ and $y=6$

Hence, the correct answer is option (b).