Rigid Transformations in Geometry - Review

​Rigid Transformations - Review

By HUNTER PARKER

Match

Match the translation type to the correct graph:

Translation

Reflection

Rotation

• Translation

• Reflection

• Rotation

​Recall:

Multiple Choice

Determine how to translate triangle ABC to triangle A'B'C'.

• (x, y) --> (x+2, y-5)

• (x, y) --> (x+2, y-9)

• (x, y) --> (x-2, y-9)

• (x, y) --> (x-2, y+9)

​Recall:

Reflections (also called "flips") can be done across the x- or y-axis. All points in the image are the same distance away from the axis on the opposite side from the pre-image.

Graphing

On the graph, choose the points created by reflecting the pre-image across the x-axis.

​Recall also:

The axis of symmetry can be any vertical or horizontal line. All points reflected from the pre-image to the image are still the same distance away from the axis.

Graphing

On the graph, choose the points created by reflecting the pre-image across the line x = 5.

​Finally, remember:

The axis of symmetry can also be a slanted line, like y = x or y = -x. Remember the shortcut of counting to the axis, then counting perpendicular:

Graphing

On the graph, choose the points created by reflecting the pre-image across the line y = -x.

​Remember rotation rules:

This is a great time to get your foldable back out to use for practice!

Graphing

On the graph, choose the points created by rotating the pre-image 90 degrees.

​Rotations can also be done around a point other than the origin.

If we choose a different point to rotate the image around, the rotation rules apply to the difference between the pre-image point and the center of rotation. This center of rotation can be a vertex of the shape or any other random point.

Graphing

On the graph, choose the points created by rotating the point (6, 7) 90°, 180°, and 270° around the point (3, 3).

Graphing

Now let's try with an entire shape!

On the graph, choose the points created by rotating the pre-image 270° around the vertex at (1, 2).

(HINT: Be sure to choose ALL THREE points, regardless of what is already there!)

Great!
Let's do some more practice!

​I am available for help.

Multiple Choice

Select the picture showing a translation of:

4 squares right and 1 square up

Graphing

Graph the coordinates for A'B'C' after a reflection over the line y=x.

Graphing

Graph the coordinates for A'B'C' after a reflection over the line y = -x.

Graphing

On the graph, choose the points created by rotating the pre-image 180° around the point (5, 0).

Graphing

On the graph, choose the points created by rotating the pre-image 90° around the vertex (-2, 1).

(HINT: Be sure to choose ALL points, regardless of what is already there!)