Exploring Reflections

A reflection is a type of transformation. Other transformations include translations, rotations, and dilations.

The result of a transformation is called the image. The original figure is called the pre-image.

Use the link below to explore reflections:

1. Click on the REFLECTION button on the left.
2. Click and drag the pre-image (the red triangle) and observe what happens.
3. Click and drag a vertex of the pre-image and observe what happens.
4. Click and drag the blue line of reflection and observe what happens.
5. Click and drag the blue point on the line of reflection and observe what happens.

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

1. When you dragged the pre-image, how did the image compare to the pre-image? What stayed the same? What changed?
2. When you dragged a vertex of the pre-image, how did the image compare to the pre-image? What stayed the same? What changed?
3. When you dragged the line of reflection, how did the image compare to the pre-image? What stayed the same? What changed?
4. 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?
5. Use the word bank to complete the sentences below:
   1. A reflection is a transformation the changes the _____________ of a figure. A translation does not change the figure’s _____________.
   2. The result of a reflection is called the ________. The ____________ figure is called the pre-image.
   3. For any reflection, the image and pre-image are ______________.
   4. 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.

WORD BANK:

image, size, opposite, congruent, distance, orientation, original, reflection

Reflections on a Coordinate Plane

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:

1. 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?
2. The reflection of triangle ABC across the y-axis could be represented using the rule (_______, _______).

Reflecting across the x-axis:

1. 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?
2. The reflection of triangle ABC across the x-axis could be represented using the rule (_______, _______).

Generating Reflections

Use the link below to explore reflections of irregular polygons:

1. Click on the ACTIVITIES button at the top of the screen.
2. 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.”