Point $A$ is located at $y$ cm and point $B$ is located at $3$ cm away from the mirror. A light beam travels $12$ cm from point $A$ to point $B$. The distance between point $A$ and $B$ is $6$ cm. Determine the $y$.
2 Answers
In the above diagram, $E$ is virtual image of $B$ in the mirror, hence $BD=ED=CF=CG=3\,$cm, $AE=12\,$cm
Now suppose $EF=GB=x\,$cm, then we have two equations for $\,x^2$
$$x^2=GB^2=AB^2-AG^2=36-(y-3)^2$$ $$x^2=EF^2=AE^2-AF^2=144-(y+3)^2$$
Thus, we can get the value of $\,y\,$ by solving
$$36-(y-3)^2=144-(y+3)^2$$
which is actually a linear equation for $\,y\,$ and obviously $\,y=9$
The answer is quite strange because if $\,y=9\,$ then $\,x=0$, so point $A$ and point $B$ are in the same vertical line
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$\begingroup$ $AG$ and $AB$ can not be equal to $6$. The problem is wrong. $\endgroup$– SeyedMar 7, 2017 at 16:34
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$\begingroup$ I agree with you, there is definitely something wrong with the dimensions here. $\endgroup$ Mar 7, 2017 at 16:37
The dimensions in this problem are wrong and it is impossible to draw it. With these dimensions there is zero centimeter between $A$ and $B$ horizontaly.