L5 Practice Part 1
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 WXYZ 180° and then translate the image horizontally 2 units to the left and vertically 3 units up. State the coordinates of each vertex of the final transformed image, W"X"Y"Z".
2.
Rotate quadrilateral PQRS 270° counterclockwise and then translate the shape horizontally 7 units to the left and vertically 4 units down. State the coordinates of each vertex of the final transformed image, P"Q"R"S".
1.
Rotate quadrilateral WXYZ 180° and then translate the image horizontally 2 units to the left and vertically 3 units up. State the coordinates of each vertex of the final transformed image, W"X"Y"Z".
Step 1: Rotation
Quadrilateral WXYZ is rotated 180° to produce image W'X'Y'Z'. 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 2 (top left), so the x values are negative and the y values are positive.
Step 2: Translation
Quadrilateral W'X'Y'Z' is translated horizontally 3 units to the left and vertically 4 units up to produce image W"X"Y"Z".
The coordinates of quadrilateral W"X"Y"Z" are W"(–5, 12), X"(–5, 8), Y"(–7, 7), Z"(–11, 8) after the rotation and translation have occurred.
Quadrilateral WXYZ is rotated 180° to produce image W'X'Y'Z'. 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 2 (top left), so the x values are negative and the y values are positive.
Step 2: Translation
Quadrilateral W'X'Y'Z' is translated horizontally 3 units to the left and vertically 4 units up to produce image W"X"Y"Z".
The coordinates of quadrilateral W"X"Y"Z" are W"(–5, 12), X"(–5, 8), Y"(–7, 7), Z"(–11, 8) after the rotation and translation have occurred.
2.
Rotate quadrilateral PQRS 270° counterclockwise and then translate the shape horizontally 7 units to the left and vertically 4 units down. State the coordinates of each vertex of the final transformed image, P"Q"R"S".
Step 1: Rotation
After quadrilateral PQRS is rotated 270° counterclockwise, image P'Q'R'S' is produced. To find the coordinates of the image, first switch the x and y values. The image is in quadrant 4 (bottom right), so the x values are positive and the y values are negative.
Step 2: Translation
Quadrilateral P'Q'R'S' is translated horizontally 7 units to the left and vertically 4 units down to produce image P"Q"R"S".
The coordinates of quadrilateral P"Q"R"S" are P"(–2, –7), Q"(0, –9), R"(–4, –11), S"(–1, –9) after the rotation and translation have been applied.
After quadrilateral PQRS is rotated 270° counterclockwise, image P'Q'R'S' is produced. To find the coordinates of the image, first switch the x and y values. The image is in quadrant 4 (bottom right), so the x values are positive and the y values are negative.
Step 2: Translation
Quadrilateral P'Q'R'S' is translated horizontally 7 units to the left and vertically 4 units down to produce image P"Q"R"S".
The coordinates of quadrilateral P"Q"R"S" are P"(–2, –7), Q"(0, –9), R"(–4, –11), S"(–1, –9) after the rotation and translation have been applied.