
# 10.5: Exercises


1. Identify the image of point P under the following transformations.
1. a translation along vector
2. a reflection across line l
3. a counterclockwise rotation of 90° about point O
4. A glide-reflection across l and along
 E O B C D l A P

1. Identify the image of point P under the following transformations.
1. a translation along vector
2. a reflection across line l
3. a counterclockwise rotation of 90° about point O
4. A glide-reflection across l and along
 D l E O C B P A

1. Identify the image of point P under the following transformations.
1. a translation along vector
2. a reflection across line l
3. a counterclockwise rotation of 90° about point O
4. A glide-reflection across l and along
 F C E O P A l B

1. Identify the image of point P under the following transformations.
1. a translation along vector
2. a reflection across line l
3. a clockwise rotation of 90° about point O
4. A glide-reflection across l and along
 C F E O P A B

1. Identify the image of point P under the following transformations.
1. a translation along vector
2. a reflection across line l
3. a clockwise rotation of 90° about point O
4. A glide-reflection across l and along
 F E P l O A B C
1. Translate the figure along vector .

1. Translate the figure along vector .
1. Translate the figure along vector .
1. Translate the figure along vector .
1. Rotate the figure 90° clockwise about the rotocenter R.
 R
 R
1. Rotate the figure 90° clockwise about the rotocenter R.
1. Rotate the figure 180° clockwise about the rotocenter R.
 R
1. Rotate the figure 180° clockwise about the rotocenter R.
 R
1. Reflect the figure over the line l.
 l
 l
1. Reflect the figure over the line l.
1. Reflect the figure over the line l.
 l
1. Reflect the figure over the line l.
 l
1. Glide-reflect the figure over the line l and along the vector .
 l
1. Glide-reflect the figure over the line l and along the vector .
 l
 l
1. Glide-reflect the figure over the line l and along the vector .
 l
1. Glide-reflect the figure over the line l and along the vector.
1. In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.

1. b.
1. In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.

1. b.
1. In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.

a. b.

1. In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.

a. b.

1. In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.

a. b.

1. In the figures below, identify the types of symmetry. If there are rotation symmetries, identify the degree(s) of rotation. If there are reflection symmetries, draw the line(s) of reflection.

a. b.

1. Enlarge the figure with respect to the point P by a factor of 2.
 P

1. Enlarge the figure with respect to the point P by a factor of 2.
 P

1. Enlarge the figure with respect to the point P by a factor of 2.
 P

1. Enlarge the figure with respect to the point P by a factor of 2.
 P

 P
1. Shrink the figure with respect to the point P by a factor of .

 P
1. Shrink the figure with respect to the point P by a factor of .

 P
1. Shrink the figure with respect to the point P by a factor of .

1. Shrink the figure with respect to the point P by a factor of .
 P

1. Triangles A and are similar and are related by the scale factor of 3.
1. If the perimeter of triangle A is 12 ft, find the perimeter of .
2. If the area of triangle A is 8 ft2, find the area of .
1. Triangles A and are similar and are related by the scale factor of 4.
1. If the perimeter of triangle A is 48 ft, find the perimeter of .
2. If the area of triangle A is 140 ft2, find the area of .
1. Triangles A and are similar and are related by the scale factor of 5.
1. If the perimeter of triangle A is 42 ft, find the perimeter of .
2. If the area of triangle A is 68 ft2, find the area of .
1. Triangles A and are similar and are related by the scale factor of 2.
1. If the perimeter of triangle A is 42 ft, find the perimeter of .
2. If the area of triangle A is 80 ft2, find the area of .
1. The shapes A and are similar.

A

8 18

1. If the perimeter of rectangle A is 22 ft, find the perimeter of .
2. If the area of rectangle A is 24 ft2, find the area of .
1. The shapes A and are similar.

A

12

18

1. If the perimeter of triangle A is 32 ft, find the perimeter of .
2. If the area of triangle A is 48 ft2, find the area of .
1. Find the value of x so that the red larger rectangle on the right is a gnomon to the blue smaller rectangle on the left.

10

4 x

1. Find the value of x so that the red L-shape is a gnomon to the blue rectangle.

8

15

1. Find the value of x so that the red triangle on the right is a gnomon to the blue triangle on the left.

9 9

6 x

1. Find the values of x and y so that the red trapezoid is a gnomon to the blue triangle.

4 5

1. Compute the values of the following.
1. Compute the values of the following.
1. Compute the values of the following using Binet’s simplified formula.
1. Compute the values of the following using Binet’s simplified formula.
1. Given and , find and .
1. Given and , find and .
1. Solve the quadratic equation .
1. Solve the quadratic equation .
1. Solve the quadratic equation .
1. Solve the quadratic equation .
1. Solve the quadratic equation .
1. Solve the quadratic equation .

10.5: Exercises is shared under a not declared license and was authored, remixed, and/or curated by Maxie Inigo, Jennifer Jameson, Kathryn Kozak, Maya Lanzetta, & Kim Sonier via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.