Transformation Properties Worksheets Grade 8

1. Emma has a triangular piece of fabric with side lengths of 7 inches, 9 inches, and 11 inches, and angles measuring 41°, 59°, and 80°. She reflects the fabric across a line. Are the side lengths and angle measures preserved after the reflection? Explain which properties of the triangle remain the same and why.
2. Noah draws a triangle with vertices at A(1, 1), B(1, 6), and C(6, 1) on a coordinate grid. He then applies a dilation centered at the origin with a scale factor of 2. After the dilation, he reflects the new triangle across the x-axis. Which properties of the original triangle are preserved through both transformations: the angle measures, the side lengths, and/or the parallelism between the sides? Explain your reasoning.
3. Aroha is designing a triangular park sign. The original triangle has side lengths of 9 cm, 13 cm, and 15 cm, and angles of 35°, 55°, and 90°. She reflects the triangle across a vertical line. Which properties of the triangle are preserved under reflection? Explain your reasoning for angles, side lengths, and whether the shape remains congruent.

…and 4 more problems

1. A rectangular garden is transformed by a scale factor of 2.5. The original garden has a length of 8 meters and a width of 6 meters. After the transformation, what is the area of the new garden in square meters?
2. A triangle has vertices at A(1, 1), B(6, 1), and C(1, 6). After a dilation with center at the origin and scale factor 2, followed by a reflection over the y-axis, which properties are preserved: angle measures, side lengths, and/or parallelism?
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 of the garden where 1 inch on the drawing represents 4 feet in the actual garden. What will be the perimeter, in inches, of the garden on his scale drawing?

…and 1 more problems

1. Liam is designing a rectangular garden with a length of 12 meters and a width of 8 meters. He wants to create a scale drawing of the garden using a scale factor of 1:50. What will be the perimeter of the garden in centimeters on his scale drawing?
2. Mere is designing a triangular logo for her school's sports day. She draws a triangle with side lengths of 30 cm, 40 cm, and 50 cm, and angles of 90°, 53°, and 37°. She then reflects the triangle across a vertical line, and then dilates the reflected image by a scale factor of 3/5, using the origin as the center of dilation. After both transformations are applied, are the angles and side lengths of the final triangle preserved compared to the original? For each property (angles and side lengths), state whether it is preserved or not, and briefly explain why.
3. (2.5 × 10³) × (4 × 10⁻²) ÷ (5 × 10²) = ?

…and 2 more problems