Scale Factors & Similar Figures: Grade 8 Quiz

A triangle has vertices at A(2, 3), B(4, 7), and C(6, 3). If triangle A'B'C' is a double prime transformation of triangle ABC with a scale factor of 2, what are the coordinates of A', B', and C'?

• A'(3, 5), B'(6, 10), C'(9, 5)

• A'(2, 3), B'(4, 7), C'(6, 3)

• A'(5, 8), B'(10, 14), C'(12, 8)

• A'(4, 6), B'(8, 14), C'(12, 6)

Two rectangles are similar. The dimensions of the first rectangle are 4 cm by 6 cm. If the scale factor to the second rectangle is 1.5, what are the dimensions of the second rectangle?

• 5 cm by 7.5 cm

• 8 cm by 12 cm

• 6 cm by 9 cm

• 4 cm by 6.5 cm

A square has a side length of 5 cm. If it undergoes a double prime transformation with a scale factor of 0.5, what will be the area of the new square?

• 6.25 cm²

• 2.5 cm²

• 12.5 cm²

• 10 cm²

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

• 200 meters

• 50 meters

• 300 meters

• 150 meters

Two circles are similar. The radius of the first circle is 3 cm. If the scale factor to the second circle is 4, what is the radius of the second circle?

• 9 cm

• 12 cm

• 6 cm

• 15 cm

A triangle has sides measuring 3 cm, 4 cm, and 5 cm. If a double prime transformation is applied with a scale factor of 3, what are the lengths of the sides of the new triangle?

• 9 cm, 12 cm, 15 cm

• 12 cm, 15 cm, 18 cm

• 6 cm, 8 cm, 10 cm

• 7 cm, 9 cm, 11 cm

A rectangular garden is 10 m long and 5 m wide. If a similar garden is created with a scale factor of 2, what will be the area of the new garden?

• 150 m²

• 50 m²

• 200 m²

• 100 m²

A triangle with vertices at (1, 1), (3, 1), and (2, 4) is transformed to triangle A'B'C' using a scale factor of 0.5. What are the coordinates of A', B', and C'?

• A'(0.5, 0.5), B'(1.5, 0.5), C'(1, 2)

• A'(1, 1), B'(2, 1), C'(2, 3)

• A'(0, 0), B'(1, 0), C'(1, 2)

• A'(1, 1), B'(3, 1), C'(2, 4)

A rectangular painting measures 20 inches by 30 inches. If it is resized to be similar with a scale factor of 0.75, what will be the new dimensions of the painting?

• 10 inches by 15 inches

• 15 inches by 22.5 inches

• 20 inches by 30 inches

• 25 inches by 37.5 inches

A right triangle has legs measuring 6 cm and 8 cm. If it undergoes a double prime transformation with a scale factor of 1.5, what will be the lengths of the legs of the new triangle?

• 6 cm and 9 cm

• 9 cm and 12 cm

• 7 cm and 10 cm

• 8 cm and 10 cm