After you have explored several reflections, answer the following questions in your math journal. Use the words pre-image and image in your responses.

When you dragged the pre-image, how did the image compare to the pre-image? What stayed the same? What changed?

When you dragged a vertex of the pre-image, how did the image compare to the pre-image? What stayed the same? What changed?

When you dragged the line of reflection, how did the image compare to the pre-image? What stayed the same? What changed?

When you dragged the point on the line of reflection, how did the image compare to the pre-image? What stayed the same? What changed?

Use the word bank to complete the sentences below:

A reflection is a transformation the changes the _____________ of a figure. A translation does not change the figure’s _____________.

The result of a reflection is called the ________. The ____________ figure is called the pre-image.

For any reflection, the image and pre-image are ______________.

Each vertex of a reflected image is exactly the same ___________ away from the line of ____________ as the corresponding vertex of the pre-image, but on the ______________ side.

Record the coordinates of the vertices of a reflected polygon as follows:

Use a capital letter for each vertex of the pre-image. For example, a triangle could have vertices at points A, B, and C.

Use corresponding capital letters to identify corresponding vertices of the image, adding a prime symbol (‘). For example, the image of the triangle with vertices A, B, and C would have vertices A’, B’, and C’.

The vertices of the image are read as follows: “A prime,” “B prime,” and “C prime.”

Watch this video to observe two different reflections on a right triangle.

Complete the following in your math journal:

Reflecting across the y-axis:

When the triangle was reflected across the y-axis, how did the coordinates of the vertices of the image compare to the corresponding coordinates of the vertices of the pre-image? Which parts stayed the same? Which parts changed? How did they change?

The reflection of triangle ABC across the y-axis could be represented using the rule (_______, _______).

Reflecting across the x-axis:

When the triangle was reflected across the x-axis, how did the coordinates of the vertices of the image compare to the corresponding coordinates of the vertices of the pre-image? Which parts stayed the same? Which parts changed? How did they change?

The reflection of triangle ABC across the x-axis could be represented using the rule (_______, _______).

Generating Reflections

Generating Reflections

Use the link below to explore reflections of irregular polygons:

Click on the ACTIVITIES button at the top of the screen.

Follow the directions for “Playing with Reflections” that appear on the right side of the screen. Then:

Check the box near the bottom left to turn the axes on.

Drag the line of reflection so that it lies exactly on top of the y-axis. Repeat steps 1 and 2 of “Playing with Reflections.”

Drag the line of reflection so that it lies exactly on top of the x-axis. Repeat steps 1 and 2 of “Playing with Reflections.”