A man starts from the point P(-3, 4) and reaches another point Q(0, 1) crossing the x-axis at R such that PR + RQ is minimum. Where is R located?

Level: Junior

Let Q' = (0, -1), the mirror image of Q in the x-axis. Observe that PR+RQ = PR+RQ'. Therefore s = PR+RQ is minimum when PQ' is a straight line l. The slope of l is (4-(-1))/(-3-0) = -5/3 and the y-intercept of l is -1. Thus the equation of l is y = (-5/3)x-1. It follows that the x-intercept of l satisfies (-5/3)x-1 = 0, or x = -3/5. R is located at (-3/5, 0).