AHSME 1969 Problem 11

Given points $P(-1,-2)$ and $Q(4,2)$ in the $xy$-plane; point $R(1,m)$ is taken so that $PR+RQ$ is a minimum. Then $m$ equals: $\text{(A) } -\tfrac{3}{5} \text{(B) } -\tfrac{2}{5} \text{(C) } -\tfrac{1}{5} \text{(D) } \tfrac{1}{5} \text{(E) either }-\tfrac{1}{5}\text{ or} \tfrac{1}{5}.$