Given points P (-1,-2) and Q (4,2) in the xy-plane, point R (1,*m*) is taken so that *m* equals:

- -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* = 4/5*x* + *b*.

Plug in Q: 2 = 4 · 4/5 + *b* = 16/5 + *b* = 10/5 → *b* = -6/5.

So line PQ is *y* = 4*x*/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).