Question

Find the foot point of $1$ from the point $(-2,3)$ to the line $2x-y-3=0$

Answer 1

We have to find the foot of perpendicular drawn from $(-2,3)$ to the line $2x-y-3=0$

So, the equation of a line perpendicular to $2x-y-3=0$ is given by $x+2y+k=0$

This line should pass through $(-2,3)$

so, $-2+2\left(3\right)+k=0⟹k=-4$

So, the equation of the perpendicular is $x+2y-4=0$

Now the foot of perpendicular is the intersection point of two lines $2x-3y=0$ and $x+2y-4=0$

Solving these two equation we get

$x=2$ and $y=-1$

Hence the coordinate of foot of perpendicular is $(2,-1)$