Lesson 5

1. Lesson 5

1.5. Explore 4

Mathematics 30-3 Module 5

Module 5: Geometry

In the next activity, you will determine the transformations used to produce some new images from an original shape.

Try This 3

In the following table, each transformed object was made by using two transformations on the original shape.

For each diagram, determine two possible sets of transformations that would produce the red shape from the blue shape. The Transformations Template provided may help you determine the transformations. The table might also help you organize your thinking.

This diagram shows a blue rectangle with vertices at (2,3), (4,3), (2,7) and (4,7). There is also a transformed red rectangle with vertices at (-4,-7), (-4,-3), (-2,-3) and (-2,-7).

Possible Set of Transformations 1:

Possible Set of Transformations 2:

This diagram shows an original figure with vertices at points (-2, 3); ( -2, 5); (-4, 3); (-4, 2); ( -5, 2); ( -5, 3); ( -6, 3); (-6, 4); ( -5, 4); (-5, 5); and (-2, 5). It also includes a transformed object with vertices at points (-6, -2); (-6, -4); (-5, -4); ( -5, -5); (-6, -5); (-6, -6); (-7, -6); ( -7, -5); ( -8, -5); and (-8, -2).

Possible Set of Transformations 1:

Possible Set of Transformations 2:

This diagram shows an original figure with vertices at points (0, 3); ( 2, -1); and (-2, -2). It also shows a transformed shape with vertices at (0, -6); (-4, 2); and (4, 4).

Possible Set of Transformations 1:

Possible Set of Transformations 2:

This diagram shows an original figure with vertices at points (4,-7); (5, -1); (6, -6); and (7, -7). It also shows a transformed shape with vertices at (-4, 7); (-3, 1); (-2, 6); and (-1, 7).

Possible Set of Transformations 1:

Possible Set of Transformations 2:

Save your responses in your course folder.

Share 2

With a partner or in a group, discuss the following questions.

Compare the strategies you used to determine the transformations used.
1. Which strategy seemed most reliable?
2. Which strategy seemed most efficient?
Which set of transformations from Try This 3 did you find the most difficult to determine? Why do you think this was the case?

If required, place a summary of your discussion in your course folder.

A rotation and translation will not work for this pair.

The order of rotating and dilating will not matter for this object.

Try using a 270° clockwise rotation.

Try a reflection across the x-axis, followed by a reflection across the y-axis.