Exercises: Distances, parallel and perpendicular lines

For instance, choose the line $g$ with $y=g(x)=x+1$ and $h$ with $y=h(x)=-x-3$. Then $m_1\cdot m_2=1\cdot (-1)=-1$and we have $g(-2)=-1$ and $h(-2)=-1$. So the point of intersection is on the two lines and they are perpendicular to each other.

Caution:

You may also choose the line $y=-1$ , which is parallel to the $x$-axis and passes through the point $(-2,-1)$ . Then there is exactly one line perpendicular to it and passing through this point, namely that one given by $x=-2$ and running parallel to the $y$- axis. However, $x=-2$ does not describe a function but a relation!