The coordinates of points P, Q, R are (-2,-3), (4,1), and (0,k). Find the value of k that minimizes PR + RQ.
+23246 The point that minimizes PR + RQ is the point on the line PRQ.
First, let's find the equation of the line: y - -3 = (1 - -3)/(4 - -2)·(x - -2)
y + 3 = (4/6)·(x + 2)
y + 3 = (2/3)·(x + 2)
For the point (0,k), x = 0: y + 3 = (2/3)·(0 + 2)
y + 3 = 4/3
y = -5/3 ---> k = -5/3
