Mastering Geometry Dilation: Graphing & Real-World Problems

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

• A'(0, 0), B'(0, 0), C'(0, 0)

• A'(2, 3), B'(4, 5), C'(3, 1)

• A'(6, 9), B'(8, 10), C'(6, 4)

• A'(4, 6), B'(8, 10), C'(6, 2)

A rectangle has a length of 6 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?

• 7 cm (length) and 4 cm (width)

• 10 cm (length) and 8 cm (width)

• 8 cm (length) and 5 cm (width)

• New dimensions are 9 cm (length) and 6 cm (width).

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

• 10 m²

• 25 m²

• 20 m²

• 16 m²

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

• 12π inches

• 9π inches

• 18π inches

• 6π inches

A garden in the shape of a triangle has an area of 24 square meters. If the garden is dilated by a scale factor of 2, what will be the area of the new garden?

• 72 square meters

• 96 square meters

• 48 square meters

• 12 square meters

A pentagon has vertices at (1, 1), (2, 3), (3, 1), (3, 2), and (1, 2). If the pentagon is dilated by a scale factor of 0.5 from the origin, what are the coordinates of the new vertices?

• [(0.5, 0.5), (1, 2), (1.5, 0.5), (1.5, 1), (0.5, 0.5)]

• [(0.5, 0.5), (1, 1), (1.5, 0.5), (1.5, 1.5), (0.5, 1)]

• [(1, 1), (2, 3), (3, 1), (3, 2), (1, 2)]

• [(0.5, 0.5), (1, 1.5), (1.5, 0.5), (1.5, 1), (0.5, 1)]

A model of a building is 10 feet tall. If the model is dilated by a scale factor of 4, how tall will the actual building be?

• 20 feet

• 40 feet

• 30 feet

• 50 feet

A triangle has sides measuring 3 cm, 4 cm, and 5 cm. If the triangle is dilated by a scale factor of 2, what will be the lengths of the sides of the dilated triangle?

• 5 cm, 6 cm, 7 cm

• The lengths of the sides of the dilated triangle are 6 cm, 8 cm, and 10 cm.

• 4 cm, 5 cm, 6 cm

• 8 cm, 9 cm, 10 cm

A rectangular swimming pool is 20 m long and 10 m wide. If the pool is dilated by a scale factor of 1.2, what will be the new area of the pool?

• 288 m²

• 240 m²

• 300 m²

• 180 m²

A logo is designed in the shape of a circle with a diameter of 10 cm. If the logo is dilated by a scale factor of 0.5, what will be the new diameter of the logo?

• 2.5 cm

• 7 cm

• 10 cm

• 5 cm