Transformation Sequences Worksheets Grade 8

1. √(169) + 4³ - (5² × 2) = ?
2. A rectangle is drawn on a coordinate plane with vertices at A(1, 2), B(4, 2), C(4, 5), and D(1, 5). It undergoes the following sequence of transformations: first, it is rotated 90° counterclockwise about the origin; then, it is reflected across the y-axis; finally, it is translated 2 units up. What are the coordinates of the final image of vertex A?
3. Liam is designing a geometric pattern for a mural. He starts with a triangle that has vertices at (2, 3), (4, 7), and (6, 1). He first translates the triangle 5 units left and 2 units up. Then he reflects the resulting shape across the y-axis. Finally, he rotates the figure 90 degrees counterclockwise about the origin. What are the coordinates of the vertices of the final triangle?

…and 4 more problems

1. A rectangular garden has a length of 15 meters and a width of 10 meters. The owner wants to create a path of uniform width around the entire garden, which will increase the total area to 266 square meters. What is the width of the path in meters?
2. A rectangle on a coordinate plane has vertices at A(1, 2), B(4, 2), C(4, 5), and D(1, 5). It undergoes the following sequence of transformations: first, it is rotated 90° counterclockwise about the origin; then, it is reflected across the y-axis; finally, it is translated 2 units up. What are the coordinates of the final image of vertex A?
3. (4² × 3) - (√144 ÷ 2) = ?

…and 4 more problems

1. A rectangle is drawn on a coordinate plane with vertices at A(1, 2), B(4, 2), C(4, 5), and D(1, 5). It undergoes the following sequence of transformations: first, it is translated 2 units right and 3 units down; then, it is reflected across the y-axis; finally, it is rotated 180° counterclockwise about the origin. What are the coordinates of the final image of vertex A?
2. Noah is creating a digital art piece using a coordinate plane. He starts with a triangle that has vertices at A(7, 12), B(13, 12), and C(10, 18). First, he dilates the triangle by a scale factor of 1/2 using the origin as the center of dilation. Then, he rotates the dilated triangle 90 degrees clockwise about the origin. Finally, he translates the rotated triangle 9 units to the left and 5 units down. What are the coordinates of vertex A after this sequence of transformations?
3. Liam is designing a logo that starts as a triangle with vertices at (2, 1), (4, 1), and (3, 4). He first translates the triangle 3 units left and 2 units up. Then he reflects the translated triangle across the y-axis. Finally, he dilates the reflected triangle by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the final triangle's vertices?

…and 4 more problems