Similarity Concepts Worksheets Grade 8

1. A triangle is drawn on a coordinate plane with vertices at A(2, 3), B(6, 3), and C(2, 7). This triangle is first reflected across the y-axis, then dilated by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the final image of vertex C after both transformations?
2. Triangle ABC has vertices A(1, 1), B(3, 1), C(1, 5). Triangle DEF has vertices D(3, 3), E(9, 3), F(3, 15). Describe a sequence of transformations that shows triangle ABC is similar to triangle DEF.
3. A rectangular garden is drawn on a coordinate plane with vertices at (2, 1), (8, 1), (8, 5), and (2, 5). The garden is dilated by a scale factor of 2.5 with the origin as the center of dilation. What are the coordinates of the vertices of the dilated garden?

…and 5 more problems

1. Liam is designing a triangular logo for his robotics team. He starts with a triangle that has vertices at (0,0), (4,0), and (0,3). He then applies a transformation that multiplies all the coordinates by 2.5. After this, he reflects the new triangle across the y-axis. What are the coordinates of the final triangle's vertices?
2. Sophia is designing a digital logo for a school event. She starts with a triangle on a coordinate grid with vertices at A(0, 0), B(14, 0), and C(0, 21). To create a similar but larger logo, she first dilates the triangle by a scale factor of 3/2 centered at the origin. Then, she translates the dilated triangle 4 units to the right and 3 units down. What are the final coordinates of vertex A?
3. Triangle ABC has vertices A(3, 5), B(7, 5), and C(3, 9). Triangle DEF has vertices D(9, 15), E(21, 15), and F(9, 27). Describe a sequence of transformations that shows triangle ABC is similar to triangle DEF.

…and 4 more problems

1. Triangle ABC has vertices A(1, 1), B(5, 1), and C(1, 5). Triangle DEF has vertices D(3, 3), E(15, 3), and F(3, 15). Describe a sequence of transformations that shows triangle DEF is similar to triangle ABC.
2. (3.6 × 10⁴) × (2.5 × 10⁻³) ÷ (1.2 × 10²) = ?
3. Triangle ABC has vertices A(9, 3), B(12, 3), and C(9, 15). Triangle DEF has vertices D(3, 1), E(4, 1), and F(3, 5). Describe a sequence of transformations (dilation and rigid motions) that maps triangle DEF onto triangle ABC.

…and 6 more problems