The pre-image ABCD has been reflected over a line of reflection, creating the image A'B'C'D'. [br][br]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.[br][br]Below, list your observations and hypothesize what you believe to be the line of reflection. [br][br][br][br]
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'. [br][br]Move the pre-image around using the blue vertices. What do you notice about these line segments? [br][br]If we had to fold this in half, where would the line of reflection be so that the image and the preimage overlap perfectly? [br][br]
Find the perpendicular bisector for the line segment AA' connecting the image to the pre-image. Make the color of this bisector green. [br][br]Find the perpendicular bisector for the line segment BB' connecting the image to the pre-image. Make the color of this bisector yellow. [br][br]Find the perpendicular bisector for the line segment CC' connecting the image to the pre-image. Make the color of this bisector purple. [br][br]Find the perpendicular bisector for the line segment DD' connecting the image to the pre-image. Make the color of this bisector brown. [br][br]Move the pre-image around. What do you notice about the perpendicular bisectors as the pre-image and image move around? [br][br]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? [br][br]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? [br][br]What property can you write to describe this relationship?