Geometry Challenges: Solving Shape Transformations

A triangle ABC is transformed to triangle A'B'C' using a double prime transformation. If the lengths of the sides of triangle ABC are 6 cm, 8 cm, and 10 cm, what are the lengths of the sides of triangle A'B'C' if it is similar to triangle ABC?

• 10k, 12k, 14k

• 6k, 8k, 12k

• 5k, 7k, 9k

• 6k, 8k, 10k (for some scale factor k)

A rectangle has dimensions of 4 m by 6 m. After a double prime transformation, the new rectangle has a length that is twice as long and a width that is half as wide. What are the dimensions of the new rectangle?

• 8 m by 4 m

• 10 m by 3 m

• 6 m by 6 m

• 12 m by 2 m

Two squares are similar, with the side length of the first square being 5 cm. If the second square is a double prime transformation of the first, and its side length is 3 cm longer than the first, what is the side length of the second square?

• 10 cm

• 8 cm

• 6 cm

• 5 cm

A parallelogram has a base of 10 m and a height of 5 m. After a double prime transformation, the base is increased by 50%. What is the new area of the parallelogram?

• 75 m²

• 50 m²

• 100 m²

• 25 m²

A triangle has vertices at (1, 2), (3, 4), and (5, 2). If this triangle is transformed using a double prime transformation to triangle A'B'C', where each vertex is moved 2 units to the right and 1 unit up, what are the coordinates of the new triangle?

• [(3, 3), (5, 5), (7, 3)]

• [(1, 3), (3, 5), (5, 3)]

• [(2, 3), (4, 5), (6, 3)]

• [(3, 2), (5, 4), (7, 2)]

A trapezoid has bases of 8 cm and 12 cm, and a height of 5 cm. If the trapezoid undergoes a double prime transformation that makes it similar to itself but with a scale factor of 2, what will be the lengths of the new bases?

• 10 cm, 14 cm

• 8 cm, 12 cm

• [16 cm, 24 cm]

• 20 cm, 30 cm

A circle has a radius of 3 cm. If it undergoes a double prime transformation that doubles its radius, what will be the circumference of the new circle?

• 12π cm

• 9π cm

• 6π cm

• 15π cm

A rhombus has diagonals of lengths 10 cm and 24 cm. If the rhombus is transformed using a double prime transformation that maintains its shape but doubles the lengths of the diagonals, what will be the area of the new rhombus?

• 360 cm²

• 480 cm²

• 240 cm²

• 120 cm²

A triangle with vertices at (0, 0), (4, 0), and (2, 3) is transformed using a double prime transformation. If the new triangle has a height that is 1.5 times the original height, what is the height of the new triangle?

• 3.0

• 4.5

• 5.0

• 6.0

A regular hexagon has a side length of 6 cm. If it undergoes a double prime transformation that triples the side length, what will be the perimeter of the new hexagon?

• 96 cm

• 90 cm

• 108 cm

• 72 cm