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?
+23246 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.
