CMOQR 2016 Problem 2

Let $P = (7, 1)$ and let $O = (0, 0)$ .

(a) If $S$ is a point on the line $y = x$ and $T$ is a point on the horizontal $x$ -axis so that $P$ is on the line segment $ST$ , determine the minimum possible area of triangle $OST$ .

(b) If $U$ is a point on the line $y = x$ and $V$ is a point on the horizontal $x$ -axis so that $P$ is on the line segment $UV$ , determine the minimum possible perimeter of triangle $OUV$ .