# Help please with reflection problem!?

A laser is shot from vertex A of square ABCD of side length 1, towards point P on BC so that BP = 3/4. The laser reflects off the sides of the square, until it hits another vertex, at which point it stops. What is the length of the path the laser takes?

Help?? Won't the laser bounce around until infinity?

1. 👍
2. 👎
3. 👁
1. No, the laser follows the old billiard table rule, that the angle of incidence is the angle of reflection.

I am going to enlarge your square to a 4 by 4, thus making your first bounce BP = 3
make a reasonable sketch, graph paper might be a good idea.
From P it will bounce and hit CD at Q
look at triangles ABP and PCQ, they are both right-angles and similar.
BP^2 + AB^2 = AP^2
9 + 16 = AP^2
AP = √25 = 5
So each triangle formed by a bounce will have the ratio
3:4:5
We are interested in the sum of the paths formed by the hypotenuses
in the second triangle PC, the short side is 1
so by ratios,
PQ/5 = 1/3
PP = 5/3
find CQ by ratios, then you can find QD

On my diagram, I have the following paths:
From A to P ---- 5 units
from P to Q on CD --- done : 5/3 units
from Q to R on AD , R is close to D,
from R to S on BC
from S to T on AB
from T to U on AD and ahhhh
from U to C , which is a vertex.
At this point you should notice that there is a lot of symmetry
and AP = RS = UC
PQ = TU
QR = TS

so once you have found QR, again by using the ratios 3:4:5
you have found the 3 different path lengths
Add up the 7 lengths, don't forget to divide by 4 , my original step to avoid some initial fractions.

1. 👍
2. 👎
2. Thank you very much it helps a lot!!

1. 👍
2. 👎
3. So, what is QR? I am a little confused...

1. 👍
2. 👎
4. For QR I got 3 1/3

1. 👍
2. 👎
5. The answer is 5.

1. 👍
2. 👎

## Similar Questions

1. ### Geometry Help?

Can anyone check my answers? * = My answer 1. Find the length of the missing side. Leave your answer in simplest radical form (1 point) The triangle is not drawn to scale. Sides 4 on the bottom and 3 on the side a. 25 b. 144 c. 5

2. ### MATH

1. Which number is a irrational number? A. 0.12 B. 0.1257486... C. 0.12121212... D. 0.111111... 2. Which number is an irrational number? A. 121/ B. 150/ C. 400/ D. 1,000,000/ 3. Which number is a perfect square? A. 32 B. 144 C.

3. ### algebra

1. find the volume of a square pyramid with side length 4 ft and a height of 9ft? 36 48** 108 144 2.find the volume of a square pyramid with side length 6 cm and a height of 2 cm? 8 12 24** 72 3.find the volume of a cone with a

4. ### Math

Point Q belongs to side AB of square ABCD. The distances from point Q to the diagonals of the square are 2 ft and 3 ft. Find the diagonal of the square.

1. ### Geometry

Quadrilateral ABCD is a parallelogram. If adjacent angles are congruent, which statement must be true? A. Quadrilateral ABCD is a square. B. Quadrilateral ABCD is a rhombus. C. Quadrilateral ABCD is a rectangle. D. Quadrilateral

2. ### Math Help!!!

please check my answers 1. Find the length of the hypotenuse of a right triangle with the legs of 9cm and 12cm A.8 B.21 C.15 *** D.225 2.The length of a hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find

3. ### Math

Trapezoid ABCD is congruent to trapezoid EFGH. Which statement is true? Trapezoid ABCD and trapezoid EFGH are shown. Trapezoid ABCD is shown with side AB measuring 15 cm, side CD measuring 9 centimeters, and the height of

4. ### Math

Square ABCD has side length 60. An ellipse E is circumscribed about the square and there is a point P on the ellipse such that PC = PD =50. What is the area of E? I got to the part with the point (30, 30). Now what next?

1. ### Math

Suzanne wants to put a fence around her square garden. If the garden covers an area of 100 ft, how many feet of fencing does she need? 20 ft*** 40 ft 10 ft 400 ft Which number is an irrational number? 0.12 0.1257486

2. ### Math

1. Rosa, Roberto, Andrea, and Inno find an estimate for square root 10. Who has proposed the best solution? (1 point) Rosa: "Use square root 9 and square root 25 to estimate." Roberto: "I will use square root 4 and square root 9."

3. ### math

The perimeter of square A is 81 inches. The length of each side of square B is 1 inch less than the length of each side of square A. One side of square B is ___ inches in length.

4. ### math

Which of the following square pyramids have a volume of 24 mm. choose all that apply a square pyramid with a side length of 9 mm and a height of 8 mm a square pyramid with a side length of 3 mm and a height of 8 mm a square