## GR 8767# 34

Forum for the GRE subject test in mathematics.
sss
Posts: 6
Joined: Sun Oct 07, 2012 5:17 pm

### GR 8767# 34

GR 8767# 34
Let the bottom edge of a rectangular mirror on a vertical wall be parallel to and h feet above the level floor. If a person with eyes t feet above the floor is standing erect at a distance d feet from the mirror, what is the relationship among h, d and t if the person can just see his own feet in the mirror?

The answer is A: t=2h and d does not matter

I feel it is like a physics problem. Do not know how to solve it.
Can anyone help me?
Thanks very much.

Legendre
Posts: 217
Joined: Wed Jun 03, 2009 1:05 am

### Re: GR 8767# 34

Its quite an unfair type of question for some people. E.g. Those who went to postgraduate studies etc, who might be out of touch with basic high school physics after so many years of not using it.

The trick is to realize that all the lengths are preserved in the mirror's reflection, and pretend the mirror is a hole into which you are looking at another object.

1) If we represent this the X,Y axis, with the line x = 0 representing the wall, and x = d representing the person. Then, the reflection of the person is the line x = -d.

2) Then, because he can just see his feet in the mirror: draw a line from the top of the person's head to the feet of his reflection. Imagine if another person is actually standing there and you can only see down to just his feet through the "hole".

3) This creates two congruent triangles. Giving the result t = 2h, regardless of d.

sss
Posts: 6
Joined: Sun Oct 07, 2012 5:17 pm

### Re: GR 8767# 34

I really forgot the physics. Thank you very much.