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Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[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

and I substituted it in the

equation. This is what I got:

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. I-Fly (2018-03-31 02:20:46)

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,136

Re: [ASK] Line of a Mirror

I think your method is good and I get 16 too.

Bob

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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob