Given points P (-1,-2) and Q (4,2) in the xy-plane, point R (1,m) is taken so that
- -3/5
- -2/5
- -1/5
- 1/5
- either -1/5 or 1/5
If PR + RQ is a minimum, then R is between P and Q, that is, it is on the segment PQ. So we tease out the equation of the line PQ:
We start with P (-1,-2), Q (4,2), and y=mx + b.
m = (2 – (-2))/(4 – (-1)) = 4/5.
So y = 4/5x + b.
Plug in Q: 2 = 4 · 4/5 + b = 16/5 + b = 10/5 → b = -6/5.
So line PQ is y = 4x/5 – 6/5.
R is (1,m), where m is the y-coordinate, not a slope m.
Then y = 4/5 · 1 – 6/5 = -2/5, so R is (1,-2/5) and our answer is (b).