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Square \(ABCD\) has a side length of \(1\), and a laser is placed at vertex \(A\). A laser beam is fired at point \(X\) on \(\overline{BX}\) so that \(BX=\frac{3}{4}\). The beam reflects off of the mirrored sides of the square, until it ends up at another vertex; at this point, the beam will stop. What is the length of the total path of the laser beam?

 

Square ABCD has a side length of 1, and a laser is placed at vertex A. A laser beam is fired at point X on BX so that BX= 3/4. The beam reflects off the mirrored sides of the square, until it ends up at another vertex; at this point, the beam will stop. What is the length of the total path of the laser beam?

 Jan 28, 2020
 #1
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The total length of the path is 7.

 Jan 28, 2020
 #2
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Great, thanks!

Guest Jan 28, 2020
 #3
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If I understand the question correctly, I have a different answer.

 

Given these points  A = (0,0)  B = (1,0)  C = (1,1)  D = (0,1)

 

The first line segment will go from point A to point X on BC with X = (1,¾).

Using the distance formula, this distance is 5/4.

 

The next line segment will go from point X to point Y or CD with Y = (2/3,1).

This distance is 5/12.

 

The next line segment will go from point Y to point Z on AD with Z = (0, ½).

This distance is 5/6.

 

The next line segment will go from point Z to point W on AB with W = (2/3,0)

This distance is 5/6.

 

The next line segment will go from point W to point V on BC with V = (1, ¼).

This distance is 5/12.

 

The next line segment will go from point V to point D (a vertex).

This distance is 5/6.

 

Adding these distances together:  5/4 + 5/12 + 5/6 + 5/6 + 5/12 + 5/4  =  5.

 Jan 28, 2020

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