Transformation Sequences Worksheets Grade 8

1. Emma is designing a logo that starts as a triangle with vertices at A(1, 2), B(3, 2), and C(2, 5). She first rotates the triangle 90° counterclockwise about the origin. Then she translates the rotated triangle 4 units to the right and 3 units down. Finally, she reflects the translated triangle across the x-axis. What are the coordinates of vertex C after this sequence of transformations?
2. Emma is designing a geometric pattern for her art project. She starts with a triangle that has vertices at A(1, 2), B(3, 2), and C(2, 4). She first rotates the triangle 90° counterclockwise about the origin. Then she translates the rotated triangle 2 units to the right and 3 units up. Finally, she reflects the translated triangle across the x-axis. What are the coordinates of vertex C after this sequence of transformations?
3. 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?

…and 2 more problems

1. A triangle has vertices at A(2, 1), B(5, 1), and C(3, 4) on a coordinate plane. It undergoes the following sequence of transformations: first, it is reflected across the x-axis; second, it is translated 3 units to the left; third, it is rotated 90° counterclockwise about the origin. What are the coordinates of the final image of vertex C?
2. (3² × 4) - √144 = ?
3. Liam is designing a rectangular garden with a length of 12 feet and a width of 8 feet. He wants to create a scale drawing where 1 inch represents 2 feet. What will be the perimeter of his scale drawing in inches?

…and 2 more problems

1. Mason is designing a digital logo for his school club. He starts with a triangle that has vertices at A(2, 7), B(7, 2), and C(7, 7). He first reflects the triangle across the y-axis. Then he rotates the reflected triangle 90° clockwise about the origin. Finally, he translates the rotated triangle 2 units left and 7 units down. What are the coordinates of vertex A after this sequence of transformations?
2. √(64) + 3² × (4 - 1) = ?
3. √(64) + 3² × (2³ - 4) = ?

…and 5 more problems