Mastering Dilation: Transforming Shapes and Coordinates

A triangle has vertices at A(2, 3), B(4, 5), and C(6, 1). If the triangle is dilated by a scale factor of 2 from the origin, what are the coordinates of the new triangle's vertices?

• A'(4, 6), B'(8, 10), C'(12, 2)

• A'(5, 7), B'(10, 12), C'(14, 4)

• A'(3, 5), B'(6, 8), C'(9, 3)

• A'(2, 3), B'(4, 5), C'(6, 1)

A rectangle has dimensions of 4 cm by 6 cm. If the rectangle is dilated by a scale factor of 1.5, what will be the new dimensions of the rectangle?

• 4 cm by 6 cm

• 7 cm by 10 cm

• 5 cm by 8 cm

• The new dimensions of the rectangle are 6 cm by 9 cm.

Two similar triangles have a ratio of 3:5. If the shorter triangle has a base of 9 cm, what is the length of the base of the larger triangle?

• 20 cm

• 12 cm

• 15 cm

• 18 cm

A square has a side length of 5 m. If it is dilated by a scale factor of 0.8, what will be the new area of the square?

• 16 m²

• 20 m²

• 25 m²

• 12.5 m²

A circle has a radius of 10 inches. If the circle is dilated by a scale factor of 0.5, what is the new radius?

• 10 inches

• 2.5 inches

• 15 inches

• 5 inches

A model of a building is 1:100 scale. If the height of the model is 2 m, what is the actual height of the building?

• 150 m

• 250 m

• 100 m

• 200 m

A triangle is dilated from a point (1, 1) with a scale factor of 3. If one vertex of the triangle is at (2, 2), what are the coordinates of the dilated vertex?

• (1, 1)

• (5, 5)

• (3, 3)

• (4, 4)

A trapezoid has bases of 8 cm and 12 cm and a height of 5 cm. If it is dilated by a scale factor of 2, what will be the new area of the trapezoid?

• 200 cm²

• 100 cm²

• 150 cm²

• 50 cm²

A pentagon is dilated by a scale factor of 0.75. If one of its sides is 10 cm long, what will be the length of that side after dilation?

• 5 cm

• 10 cm

• 12.5 cm

• 7.5 cm

A triangle with vertices at (0, 0), (2, 0), and (1, 2) is dilated by a scale factor of 4. What are the coordinates of the new triangle's vertices?

• (0, 0), (4, 0), (2, 4)

• (0, 0), (6, 0), (3, 6)

• The new triangle's vertices are (0, 0), (8, 0), and (4, 8).

• (0, 0), (10, 0), (5, 10)