Geometry problem

[Rachiesweet14]

Find the coordinates of the endpoints O(0,0) and P(3,2) of line OP after two reflections, the first one over the line y=1 and the second over the line y=5. What transformation is the composition of these two reflections? Write a rule in the form (x,y)---->( , ) to summarize this transfomation.

 

[soroban]

Hello, Rachiesweet14!

\(\displaystyle \text{Find the coordinates of the endpoints O(0,0) and P(3,2) of line OP after two reflections:}\)
\(\displaystyle \text{the first one over the line }y=1\text{ and the second over the line }y=5.\)
\(\displaystyle \text{What transformation is the composition of these two reflections? }\)
\(\displaystyle \text{Write a rule in the form }(x,y) \to (?,?)\text{ to summarize this transfomation.}\)

Making a sketch will certainly help . . .


\(\displaystyle (x,\,y) \;\to\; \underbrace{(x,\,2-y)}_{\text{over }y\,=\,1} \;\to\; \underbrace{(x,\,y+8)}_{\text{over }y\,=\,5}\)

 

[Rachiesweet14]

Hello, Rachiesweet14!


Making a sketch will certainly help . . .


\(\displaystyle (x,\,y) \;\to\; \underbrace{(x,\,2-y)}_{\text{over }y\,=\,1} \;\to\; \underbrace{(x,\,y+8)}_{\text{over }y\,=\,5}\)

I sketched it out but i dont get how to reflect it. Do you mind showing me your sketch?

 

[Mrspi]

I sketched it out but i dont get how to reflect it. Do you mind showing me your sketch?

This website has GREAT animated examples to show what happens in this type of composition of reflections:

http://www.mathwarehouse.com/transformations/reflections-theorem.php