Transformation Properties Worksheets Grade 8

1. A rectangular solar panel has a length of 3.6 × 10^2 centimeters and a width of 2.5 × 10^1 centimeters. When installed, it is enlarged using a scale factor of 4. What is the area of the enlarged solar panel in square centimeters? Express your answer in scientific notation.
2. A triangular garden is drawn on a coordinate plane with vertices at A(2, 3), B(6, 3), and C(4, 7). The triangle is first reflected across the x-axis, then translated 4 units to the left. What are the coordinates of vertex C after both transformations?
3. A scientist is studying bacteria growth in a lab. The initial population is 500 bacteria, and it doubles every 3 hours. The scientist uses the exponential growth formula P = 500 × 2^(t/3), where P is the population and t is time in hours. After how many hours will the bacteria population reach 8,000?

…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. 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?
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?

1. Aroha is an artist creating a design using a triangular piece of stained glass. The triangle has vertices at points A(1, 3), B(5, 3), and C(3, 7). She first reflects the triangle across the x-axis. Then she dilates the reflected triangle by a scale factor of 3, with the origin as the center of dilation. After these two transformations, does the final triangle preserve the original triangle's angle measures and side lengths? Explain your reasoning and state which properties are preserved and which are not.
2. A triangle has vertices at (2, 7), (7, 12), and (12, 7). After a dilation with center at the origin and scale factor 2, what properties are preserved? Check if the angles are preserved and if the side lengths are preserved. State your answer as 'angles preserved, distances not preserved' or 'angles not preserved, distances preserved' or 'both preserved' or 'neither preserved'.
3. A rectangular swimming pool is being designed for a community center. The pool's length is 25 meters and its width is 15 meters. The designers want to create a scale model where 1 centimeter represents 2.5 meters. What will be the perimeter of the pool in centimeters on the scale model?

…and 2 more problems