Question

Find the projection of the point $(1,0)$ on the line joining the points $P(-1,2)$ and $Q(5,4)$.

Answer 1

Line $PQ$ is $x-3y+7=0$ and the line through $(1,0)$ perpendicular to it is $3x+y-3=0$. Solving we get the foot of perpendicular as $(1/5,12/5)$ which is the projection of $(1,0)$ on the given line.