We are doing basic geometric constructions in class, and I have a problem on my hw that I dont know how to do. Please see the attached sheet if you can help. Thanks
Hello, igottaquestion!
Mark is standing at G.
There is a chair H in the next room
and a mirror CD on the wall.
By looking in the mirror, can Mark see the chair?
Justify your answer.
Construct the line of sight from G to the mirror to H.Code:C D * - - - - * - - * - - - * | | | | | | | | | o G | | | | * - - o - - * - - - - - * H
Draw HP perpendicular to the far wall.
Extend HP to Q so that PQ = HP.
Draw line GQ, intersecting the far wall at X.If point $\displaystyle X$ occurs on the mirror $\displaystyle (CD)$,Code:Qo :\ : \ : \ : \ P: \ X * - - o - - o - - - - - * | : \ | | : \ | | : | \ | | : | oG | | : | | * - - o - - * - - - - - * H
. . Mark can see the chair.
Justification: Draw line segment $\displaystyle HX.$The line of sight is: .$\displaystyle GX + XH$Code:Qo :\ : \ : \ : \ P: θ\ X * - - o - - o - - - - - * | : α/ \β | | : / \ | | : / \ | | : / oG | | :/ | * - - o - - * - - - - - * H
Right triangles $\displaystyle QPX$ and $\displaystyle HPX$ are congruent.
. . Hence: .$\displaystyle \angle \alpha = \angle\theta$
$\displaystyle \angle\theta$ and $\displaystyle \angle\beta$ are vertical angles.
. . Hence: .$\displaystyle \angle\theta = \angle\beta$
Therefore: .$\displaystyle \angle\alpha \,=\,\angle\beta$
The angle of incidence equals the angle of reflection.
I answered this for him elsewhere, but gave the hint, the same method you used here, rather than simply do his homework for him. You spoil everyone else's efforts by this practice, and incidentally spoil the efforts of conscientious students who do their own work! Perhaps you saw my hint? What good is it for the rest of us to try to guide him if you butt in, simply fluffing your own feathers?
You might think that you are helping, but you are not. You won't be there at exam time. If he wants to learn to play baseball, he has to pick up the bat, not just watch you hit home runs. You do this in every single forum that you attend, and it's extremely annoying for us to see our own efforts sabotaged like this.
It is MHF policy that members do not provide further help or solutions when someone is already helping a member and is waiting for the OP to give feedback. Infractions are given for violating this policy. Having said this, I give the benefit of the doubt to Soroban that your efforts (which I greatly appreciate, by the way) elsewhere was not seen by him in this instance. I sincerely hope I am correct in doing so .....
MHF strongly encourages that hints rather than complete solutions be given. Having said this, there are some members who feel that providing complete solutions is more beneficial. This style of help is not condoned by the majority - and I personally do not agree with it either - but it is not currently illegal. It is something that gets debated from time to time, and will continue to be debated.