L4 Practice Part 2
Completion requirements
Unit A: Geometry
Chapter 2: Transformations
Practice
Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You
will learn the material more thoroughly if you complete the questions before checking the answers.
1.
Rotate quadrilateral LMNO 90Β° counterclockwise about the origin.
a.
State the coordinates of the image, quadrilateral L'M'N'O'.
b.
Draw and label image L'M'N'O'.
2.
Rotate ΞDEF 180Β° clockwise about the origin.
a.
State the coordinates of the image, D'E'F'.
b.
Draw and label the image, ΞD'E'F'.
3.
Answer the following questions for the diagram below.
- Is the transformation a rotation? If a rotation did occur, state the degree and direction.
- If it is not a rotation, state the type of transformation that occurred (translation and/or reflection).
4.
Answer the following questions for the diagram below.
- Is the transformation a rotation? If a rotation did occur, state the degree and direction.
- If it is not a rotation, state the type of transformation that occurred (translation and/or reflection).
5.
Answer the following questions for the diagram below.
- Is the transformation a rotation? If a rotation did occur, state the degree and direction.
- If it is not a rotation, state the type of transformation that occurred (translation and/or reflection).
1.
Rotate quadrilateral LMNO 90Β° counterclockwise about the origin.
a.
State the coordinates of the image, quadrilateral L'M'N'O'.
b.
Draw and label image L'M'N'O'.
a.
Step 1: Write the coordinate of the original quadrilateral: L(2, 7), M(5, 10), N(5, 4), O(4, 8).
Step 2: Determine which quadrant the image will appear in. After the 90Β° rotation counterclockwise (to the left), the image will be in quadrant 2. In quadrant 2, the x values are negative and the y values are positive.
Step 3: Switch the x and y values in each coordinate. Include the correct signs based on the location of the image. The coordinates for the image are L'(β7, 2), M'(β10, 5), N'(β4, 5), O'(β8, 4).
Step 2: Determine which quadrant the image will appear in. After the 90Β° rotation counterclockwise (to the left), the image will be in quadrant 2. In quadrant 2, the x values are negative and the y values are positive.
Step 3: Switch the x and y values in each coordinate. Include the correct signs based on the location of the image. The coordinates for the image are L'(β7, 2), M'(β10, 5), N'(β4, 5), O'(β8, 4).
b.
2.
Rotate ΞDEF 180Β° clockwise about the origin.
a.
State the coordinates of the image, D'E'F'.
b.
Draw and label the image, ΞD'E'F'.
a.
Step 1: Write the coordinates of ΞDEF: D(β8, β2), E(β3, β1), F(β2, β5).
Step 2: Determine which quadrant the image will appear in. After the 180Β° rotation clockwise (to the right), the image will be in quadrant 1. In quadrant 1, the x and y values are positive.
Step 3: When a 180Β° rotation occurs, x and y values of the image remain the same as the original point; however, the signs of the x and y values of the image are opposite to the x and y values of the original point. The coordinates of the image are D(8, 2), E(3, 1), F(2, 5).
Step 2: Determine which quadrant the image will appear in. After the 180Β° rotation clockwise (to the right), the image will be in quadrant 1. In quadrant 1, the x and y values are positive.
Step 3: When a 180Β° rotation occurs, x and y values of the image remain the same as the original point; however, the signs of the x and y values of the image are opposite to the x and y values of the original point. The coordinates of the image are D(8, 2), E(3, 1), F(2, 5).
b.
3.
Answer the following questions for the diagram below.
- Is the transformation a rotation? If a rotation did occur, state the degree and direction.
- If it is not a rotation, state the type of transformation that occurred (translation and/or reflection).
Step 1: Identify and label the corresponding points on the image.
Step 2: The coordinates of quadrilateral ABCD are A(β7, 1), B(β4, 6), C(β2, 4), D(β3, 2). The coordinates of image A'B'C'D' are A'(1, 7), B'(6, 4), C'(4, 2), D'(2, 3). The image, quadrilateral A'B'C'D', has a different orientation (direction) than quadrilateral ABCD.
A rotation has occurred.
Step 3: The x and y values are switched, so the image is formed by a 90Β° or 270Β° rotation. The image is produced by a 270Β° rotation counterclockwise or 90Β° rotation clockwise about the origin.
Step 2: The coordinates of quadrilateral ABCD are A(β7, 1), B(β4, 6), C(β2, 4), D(β3, 2). The coordinates of image A'B'C'D' are A'(1, 7), B'(6, 4), C'(4, 2), D'(2, 3). The image, quadrilateral A'B'C'D', has a different orientation (direction) than quadrilateral ABCD.
A rotation has occurred.
Step 3: The x and y values are switched, so the image is formed by a 90Β° or 270Β° rotation. The image is produced by a 270Β° rotation counterclockwise or 90Β° rotation clockwise about the origin.
4.
Answer the following questions for the diagram below.
- Is the transformation a rotation? If a rotation did occur, state the degree and direction.
- If it is not a rotation, state the type of transformation that occurred (translation and/or reflection).
Step 1: Label the corresponding points on the image.
Step 2: Since each corresponding point in quadrilateral ABCD and its image, quadrilateral A'B'C'D', are the same distance from the x-axis, a reflection in the x-axis has occurred.
Step 2: Since each corresponding point in quadrilateral ABCD and its image, quadrilateral A'B'C'D', are the same distance from the x-axis, a reflection in the x-axis has occurred.
5.
Answer the following questions for the diagram below.
- Is the transformation a rotation? If a rotation did occur, state the degree and direction.
- If it is not a rotation, state the type of transformation that occurred (translation and/or reflection).
Step 1: Label the corresponding points on the image.
Step 2: The image, quadrilateral A'B'C'D', has the same orientation (direction) as quadrilateral ABCD. Therefore, a rotation did not occur.
Step 3: A translation of 12 units to the right and 8 units down has taken place.
Step 2: The image, quadrilateral A'B'C'D', has the same orientation (direction) as quadrilateral ABCD. Therefore, a rotation did not occur.
Step 3: A translation of 12 units to the right and 8 units down has taken place.