- #1

Monoxdifly

MHB

- 284

- 0

A. 4y + x - 15 = 0

B. 4y + x - 9 = 0

C. 4y + x + 15 = 0

D. 4y - x - 15 = 0

E. 4y - x - 9 = 0

Since I didn't know how to approach the problem in a formal, textbook way, I tried to get... creative. The point of reflection must be exactly in the middle of (3, -1) and (5, 7), that is, (4, 3). Since the mirror must be a line perpendicular to BB' (which has the slope 4) and going through (4, 3), the slope of the mirror is \(\displaystyle -\frac{1}{4}\) and I substituted it in the \(\displaystyle y-y_1=m(x-x_1)\) equation. This is what I got:

\(\displaystyle y-3=-\frac{1}{4}(x-4)\)

4(y - 3) = -(x - 4)

4y - 12 = -x + 4

4y + x - 12 - 4 = 0

4y + x - 16 = 0 which is not in any of the options, but really close to the option A. Can we just assume that the option A was a typo? Or did I make a mistake somewhere?