Warm-Up

• Reflect the figure across the y-axis. Label the image A’B’C’.

• Translate the newimage using the vector <2,-10>. Label the final image A’’B’’C’’.

Homework Review 7.1 and 7.2

Homework Review 7.1 and 7.2

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Homework Review 7.1 and 7.29.

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Homework Review 7.1 and 7.2

Homework Review 7.1 and 7.2

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7.3 Composition of Transformations

Minimal Path

Finish Section 7.2 – Minimal Path

• Step 1 Reflect the ___________ point over the wall. (Label as ______’.)

• Step 2 Connect the ___________ point to the reflected point.

• Step 3 Connect the ___________ point to where Step 2 intersects the wall.

• Step 4 Add __________________ to show direction!

Example A: Pool TableFind the minimal path FROM point A to point B bouncing off the BOTTOM wall.

Example B: Highway

Compositions of Transformations:

Draw triangle ABC with vertices:

A (-1 , 0), B (4 , 0), and C (2 , 6)

Translate ABC by the rule:

(x , y) (x – 6 , y – 5)

Translate the new image (A’B’C’) by the rule:

(x , y) (x + 14 , y + 3)

a. What single translation is equivalent to the composition of these two translations?

b. What single translations brings the second image A’’B’’C’’ back to the position of the original triangle ABC?

Practice:

1. Name a single translation that is the equivalent to the composition of these two translation vectors:

< +2, -3> and < +5, +7>

2. Name a single rotation that is the combination of these three rotations:

40° clockwise, 50° counter-clockwise, 75° clockwise

3. If a figure is translated using the vector< 4, -7> and then translated again using < 5, -7>, this can be represented by what single vector?

4. A rotation 40° clockwise, followed by a rotation 30° counter-clockwise, followed by a rotation 20° clockwise is equivalent to what single rotation?

• Reflections Across Parallel Lines Conjecture: A composition of two reflections across two parallel lines is equivalent to a single _________________________________.

• In addition, the distance from any point to its second image under the two reflections is _________________ the distance between the parallel lines.

Practice:

Name a single transformation that can replace the following two transformations: reflection across line p, then reflection across line q, if lines p and q are vertical and 10 inches apart. (HINT: Draw a picture!)

Name a single transformation that can replace a reflection over the x-axis followed by the translation <0,-3>. (HINT: Plot a few points, perform the transformations, and look for a pattern!)

• A glide reflection is a composition of a ________________ and a ________________.

7.3 Compositions of Transformations

• Homework

▫ Worksheet 7.3