Reflections
Standard
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Goals for this section:
To understand that reflections should be intuitive. Reflecting across a line will result in a mirror image.
This notation means: P reflected about the line m is P'
- R is the reflection
- m is the line we reflect about
What do we mean reflected about the line m?
The point (2,4) is being reflected about the line y=x. Its reflection is (4,2)
The point (-1,2) is being reflected about the line x = 0 (or the y-axis). Its refelction is (1,2)
Example
Point P has coordinates (3,4). If Rx=1(P) = P’, what are the coordinates of P'?
This means, "What's the reflection of Point P about the line x = 1?" Remember, x = 1 is a vertical line. So x = 1 is the mirror that (3,4) is looking at.
How far away is (3,4) from the line? It's 2 units away, so its reflection will be 2 units away from the line as well, but on the other side. The coordinate will be (-1, 4).