Exploring and Investigating Reflection Properties

The pre-image ABCD has been reflected over a line of reflection, creating the image A'B'C'D'. Use the blue vertices on the pre-image ABCD and observe what happens to the image A'B'C'D' as ABCD is moved around. Below, list your observations and hypothesize what you believe to be the line of reflection.

Create line segments connecting the vertex of the pre-image to its corresponding vertex on the image, i.e. create segments AA', BB', CC', and DD'. Move the pre-image around using the blue vertices. What do you notice about these line segments? If we had to fold this in half, where would the line of reflection be so that the image and the preimage overlap perfectly?

Find the perpendicular bisector for the line segment AA' connecting the image to the pre-image. Make the color of this bisector green. Find the perpendicular bisector for the line segment BB' connecting the image to the pre-image. Make the color of this bisector yellow. Find the perpendicular bisector for the line segment CC' connecting the image to the pre-image. Make the color of this bisector purple. Find the perpendicular bisector for the line segment DD' connecting the image to the pre-image. Make the color of this bisector brown. Move the pre-image around. What do you notice about the perpendicular bisectors as the pre-image and image move around? Create a property to describe the relationship you found.

Measure the distance from each vertex on the image and pre-image to the perpendicular bisectors. What do you notice? If you change the image and corresponding preimage, does the relationship you found on the original image and preimage stay the same? If yes, create a property that could describe this relationship.

After finding the properties relating to the perpendicular bisector, where do you think the line of reflection might be? Explain your reasoning.

Create a function in two-variables F(x,y)--> ( , ) for the reflection above.

Provide the domain and range of the function for the reflection in the image above.

Are the image and pre-image congruent? How do you know? What property can you write to describe this relationship?