Dilation Adventures: Solving Geometry Challenges

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: 12 cm, Width: 6 cm

• Length: 15 cm, Width: 7 cm

• Length: 8 cm, Width: 4 cm

• Length: 10 cm, Width: 5 cm

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

• 2.5 m²

• 6.25 m²

• 12.5 m²

• 10 m²

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

• 10 feet

• 7 feet

• 8 feet

• 9 feet

A triangle with vertices at (2, 3), (4, 5), and (2, 7) is dilated by a scale factor of 4. What are the coordinates of the new vertices?

• (10, 15), (20, 25), (10, 30)

• (4, 6), (8, 10), (4, 14)

• (6, 9), (12, 14), (6, 28)

• The new vertices are (8, 12), (16, 20), and (8, 28).

A rectangular pool measures 10 m by 5 m. If the pool is dilated by a scale factor of 2, what will be the perimeter of the new pool?

• 60 m

• 70 m

• 50 m

• 40 m

A pentagon has sides measuring 3 cm each. If the pentagon is dilated by a scale factor of 2, what will be the total length of the sides of the new pentagon?

• 30 cm

• 15 cm

• 20 cm

• 25 cm

A trapezoid has bases of 8 cm and 4 cm, and a height of 3 cm. If it is dilated by a scale factor of 1.5, what will be the area of the new trapezoid?

• 36 cm²

• 24 cm²

• 40.5 cm²

• 18 cm²

A triangle has an area of 12 square units. If it is dilated by a scale factor of 3, what will be the area of the new triangle?

• 108 square units

• 72 square units

• 24 square units

• 36 square units

A rectangle is dilated from a scale factor of 0.75. If the original rectangle has an area of 32 square units, what will be the area of the dilated rectangle?

• 16 square units

• 18 square units

• 12 square units

• 24 square units