March 31st, 2018, 06:18 AM  #1 
Senior Member Joined: Nov 2010 From: Indonesia Posts: 2,001 Thanks: 132 Math Focus: Trigonometry  [ASK] Line of a Mirror
The point B(3, 1) is reflected by the line g and results in B'(5, 7). The equation of line g is .... 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 $\displaystyle yy_1=m(xx_1)$ equation. This is what I got: $\displaystyle y3=\frac{1}{4}(x4)$ 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? Last edited by Monox D. IFly; March 31st, 2018 at 06:21 AM. 

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