# Transformations - Practice #3 (Grade 10)

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## Transformations - Practice #3

1.

The following pre-image is rotated 90° counterclockwise about the origin, and then translated 5 units to the right and 2 units down. Draw the correct transformed image.

2.

The following pre-image is rotated 180° about the origin clockwise, then translated 3 units in the x direction and -4 units in the y direction. Draw the correct transformed image.

3.

Which of these transformations is not rigid?

- Translate 4 to the left and rotate [math]180 deg[/math]
- Reflect across the [math]x[/math] axis and translate down by 6
- Rotate [math]90 deg[/math] clockwise and dilate by a factor of 2
- Translate down 2, reflect across the [math]y[/math] axis, and rotate [math]180 deg[/math]

4.

The transformation between the two graphs is best described as

- translation
- rotation
- reflection
- reflection and rotation

5.

Point A'(12,4) is the image of point A(3,1) under a dilation with respect to the origin. What is the constant of dilation?

- 9
- [math]1/4[/math]
- 3
- 4

6.

What is the largest angle of rotation that can be used to map a regular octagon back onto itself without completing a full rotation?

- 270
- 45
- 315
- 180

7.

Find the single translation that has the same effect as each of the following composition of translations.

a) [math]T_{1,5} " followed by " T_{-4,7}[/math]

b) [math]T_{-4,-6} " followed by " T_{-2,1}[/math]

a) [math]T_{1,5} " followed by " T_{-4,7}[/math]

b) [math]T_{-4,-6} " followed by " T_{-2,1}[/math]

8.

The regular pentagon ABCDE is divided into five congruent triangles. The 3rd vertex of each of these triangles (not on the sides of the pentagon) meets at the center of pentagon ABCDE; call this point X.

a) Name the image of point D under a 144 degree counter-clockwise rotation about X.

b) What is the image of any point under a 360 degree counter-clockwise rotation about X?

a) Name the image of point D under a 144 degree counter-clockwise rotation about X.

b) What is the image of any point under a 360 degree counter-clockwise rotation about X?

9.

Sketch Triangle ABC with vertices A(1,2); B(-3,-1); C(0,3). Find the image of Triangle ABC under the following glide reflections.

a) [math]T_{-1,1} and r_{y = 0}[/math]

b) [math]T_{-2,0} and r_{x = -1}[/math]

a) [math]T_{-1,1} and r_{y = 0}[/math]

b) [math]T_{-2,0} and r_{x = -1}[/math]

10.

For triangle ABC, with corresponding vertices (3, 2), (4, -1), (-1, 1), find the vertices of the transformed triangle, A'B'C', after a translation of 2 units right, 3 units down, and then a reflection over the y-axis.

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