Dilation in Geometry: Transforming Shapes and Sizes

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, what are the coordinates of the new triangle A', B', and C'?

• A'(5, 8), B'(10, 12), C'(14, 4)

• A'(3, 5), B'(6, 7), C'(9, 3)

• A'(4, 6), B'(8, 10), C'(12, 2)

• A'(2, 3), B'(4, 5), C'(6, 1)

A rectangle has a length of 8 cm and a width of 4 cm. If the rectangle is dilated by a scale factor of 1.5, what will be the new dimensions of the rectangle?

• Length: 14 cm, Width: 7 cm

• Length: 12 cm, Width: 6 cm

• Length: 10 cm, Width: 5 cm

• Length: 8 cm, Width: 4 cm

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

• 18 cm

• 20 cm

• 15 cm

• 12 cm

A square has a side length of 10 m. If it is dilated by a scale factor of 0.5, what will be the area of the new square?

• 10 m²

• 25 m²

• 100 m²

• 50 m²

A circle has a radius of 6 inches. If the circle is dilated by a scale factor of 3, what will be the new radius?

• 24 inches

• 12 inches

• 30 inches

• 18 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?

• 75 m

• 50 m

• 150 m

• 200 m

A triangle is dilated from a scale factor of 4. If one side of the original triangle is 5 cm, what is the length of the corresponding side in the dilated triangle?

• 10 cm

• 20 cm

• 25 cm

• 15 cm

A photograph is enlarged by a scale factor of 2. If the original dimensions are 5 inches by 7 inches, what are the dimensions of the enlarged photograph?

• 8 inches by 10 inches

• 12 inches by 14 inches

• 10 inches by 14 inches

• 5 inches by 7 inches

A garden is in the shape of a rectangle measuring 12 m by 8 m. If the garden is enlarged by a scale factor of 2, what will be the new area of the garden?

• 96 m²

• 144 m²

• 256 m²

• 384 m²

A map is drawn to a scale of 1:25000. If a distance on the map measures 4 cm, what is the actual distance represented on the ground?

• 2 km

• 500 m

• 1 km

• 1.5 km