Question

Find the coordinates of foot of the perpendicular drawn from the point $(2,3)$ to the line $x+y+1=0$.

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

Answer 1

The correct option is C $(-1,0)$

Given line is $x+y+1=0$ .....(1)

Let the foot of the perpendicular of the point $(2,3)$ be $D(x_1,y_1)$.

Slope of the line $x+y+1=0$ is $m_1=-1$.

Slope of the perpendicular is $1$.

$m_2=1$

Equation of the perpendicular line passing through $(2,3)$ will be :

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

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

Now finding the intersection of the lines $y-x=1$ and $x+y+1=0$, we get,

$x=-1,y=0$

Hence, foot of perpendicular will be $(-1,0)$.