L5 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.
a.
Rotate quadrilateral FGHI 180° and then reflect the image F'G'H'I' in the x-axis. State the coordinates of each vertex for the image, F"G"H"I".
b.
Instead of performing two transformations—a rotation and then reflection—what single transformation could be applied to quadrilateral FGHI produce quadrilateral F"G"H"I"?
1.
a.
Rotate quadrilateral FGHI 180° and then reflect the image F'G'H'I' in the x-axis. State the coordinates of each vertex for the image, F"G"H"I".
b.
Instead of performing two transformations—a rotation and then reflection—what single transformation could be applied to quadrilateral FGHI produce quadrilateral F"G"H"I"?
a.
Step 1: Rotation
Quadrilateral FGHI is rotated 180° to produce image F'G'H'I'. Recall that when a polygon is rotated 180°, it will be the same whether it is rotated in the clockwise or counterclockwise direction.
When a 180° rotation occurs, the 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 image is in quadrant 3 (bottom left), so the x values are negative and the y values are negative.
Step 2: Reflection
Reflect quadrilateral F'G'H'I' in the x-axis to produce image F"G"H"I".
The coordinates of quadrilateral F"G"H"I" are F"(–2, 10), G"(–11, 7), H"(–8, 2), I"(–4, 3) after the rotation and reflection are applied.
Quadrilateral FGHI is rotated 180° to produce image F'G'H'I'. Recall that when a polygon is rotated 180°, it will be the same whether it is rotated in the clockwise or counterclockwise direction.
When a 180° rotation occurs, the 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 image is in quadrant 3 (bottom left), so the x values are negative and the y values are negative.
Step 2: Reflection
Reflect quadrilateral F'G'H'I' in the x-axis to produce image F"G"H"I".
The coordinates of quadrilateral F"G"H"I" are F"(–2, 10), G"(–11, 7), H"(–8, 2), I"(–4, 3) after the rotation and reflection are applied.
b.
When quadrilateral FGHI is reflected in the y-axis, the same image as F"G"H"I" is produced.