Mastering Geometry Dilation and Scale Factors for Grade 8

A rectangle has a length of 4 cm and a width of 2 cm. If the rectangle is dilated by a scale factor of 3, what will be the new dimensions of the rectangle?

• Length: 10 cm, Width: 5 cm

• Length: 8 cm, Width: 4 cm

• Length: 12 cm, Width: 6 cm

• Length: 15 cm, Width: 7 cm

A triangle has vertices at (1, 2), (3, 4), and (5, 2). If the triangle is dilated from the origin by a scale factor of 2, what are the coordinates of the new vertices?

• (2, 2)

• (4, 6)

• (8, 2)

• [(2, 4), (6, 8), (10, 4)]

A square has a side length of 5 m. If it is dilated by a scale factor of 0.5, what will be the area of the new square?

• 6.25 m²

• 10 m²

• 2.5 m²

• 12.5 m²

A circular garden has a radius of 6 feet. If the garden is enlarged by a scale factor of 1.5, what will be the new radius of the garden?

• 7 feet

• 12 feet

• 9 feet

• 10 feet

A model of a car is built at a scale of 1:10. If the actual car is 4 meters long, how long is the model car?

• 0.4 meters

• 1 meter

• 0.2 meters

• 0.8 meters

A triangle has sides measuring 6 cm, 8 cm, and 10 cm. If the triangle is dilated by a scale factor of 0.75, what are the lengths of the sides of the new triangle?

• 6 cm, 8 cm, 10 cm

• 4.5 cm, 6 cm, 7.5 cm

• 3 cm, 4 cm, 5 cm

• 5 cm, 7 cm, 9 cm

A photograph is enlarged from a size of 8 inches by 10 inches to a size of 16 inches by 20 inches. What is the scale factor of the enlargement?

• 2

• 1

• 4

• 3

A rectangular swimming pool is 12 m long and 6 m wide. If the pool is to be enlarged by a scale factor of 2, what will be the new area of the pool?

• 288 m²

• 180 m²

• 72 m²

• 144 m²

A piece of artwork is 24 inches wide and 36 inches tall. If it is reduced by a scale factor of 0.25, what will be the new dimensions of the artwork?

• 4 inches wide and 6 inches tall

• 6 inches wide and 9 inches tall

• 8 inches wide and 12 inches tall

• 12 inches wide and 18 inches tall

A triangular plot of land has a base of 10 m and a height of 5 m. If the plot is dilated by a scale factor of 4, what will be the area of the new triangular plot?

• 200 m²

• 400 m²

• 50 m²

• 100 m²