Exploring Transformations: Analyze and Solve in Geometry

A triangle is reflected over the y-axis. If the original triangle has vertices at (2, 3), (4, 5), and (3, 1), what are the coordinates of the reflected triangle?

• [(-2, 3), (-4, 5), (-3, 1)]

• (3, 1)

• (2, -3)

• (4, -5)

A rectangle is translated 5 units to the right and 3 units up. If the original rectangle has vertices at (1, 2), (1, 4), (3, 2), and (3, 4), what are the coordinates of the new rectangle?

• (1, 2), (1, 4), (3, 2), (3, 4)

• (6, 2), (6, 4), (8, 2), (8, 4)

• The new rectangle has vertices at (6, 5), (6, 7), (8, 5), and (8, 7).

• (5, 5), (5, 7), (7, 5), (7, 7)

A square is rotated 90 degrees clockwise around the origin. If the square has vertices at (1, 1), (1, 3), (3, 1), and (3, 3), what are the coordinates of the rotated square?

• [(1, 1), (3, 1), (1, 3), (3, 3)]

• [(1, 2), (3, 2), (1, 4), (3, 4)]

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

• [(0, 1), (0, 3), (2, 1), (2, 3)]

A point (x, y) is dilated by a scale factor of 2 from the origin. If the original point is (3, 4), what are the coordinates of the dilated point?

• (6, 8)

• (3, 8)

• (0, 0)

• (4, 6)

A trapezoid is reflected over the line y = x. If the trapezoid has vertices at (2, 3), (4, 3), (5, 1), and (1, 1), what are the coordinates of the reflected trapezoid?

• [(3, 2), (3, 4), (1, 5), (1, 1)]

• (1, 2)

• (5, 3)

• (2, 4)

A circle with a radius of 4 is translated 2 units left and 3 units down. What is the center of the new circle if the original circle is centered at (5, 5)?

• (2, 2)

• (5, 5)

• (4, 3)

• (3, 2)

A pentagon is rotated 180 degrees around the point (0, 0). If the pentagon has vertices at (2, 3), (4, 5), (6, 1), (3, 2), and (1, 4), what are the coordinates of the rotated pentagon?

• [-2, -5]

• [-4, -3]

• [-1, -1]

• [[-2, -3], [-4, -5], [-6, -1], [-3, -2], [-1, -4]]

A figure is dilated by a scale factor of 0.5. If the original figure has vertices at (6, 8), (8, 10), and (10, 6), what are the coordinates of the dilated figure?

• [(3, 5), (5, 7), (7, 3)]

• [(2, 4), (4, 6), (6, 2)]

• [(3, 4), (4, 5), (5, 3)]

• [(1, 2), (2, 3), (3, 1)]

A parallelogram is translated 4 units left and 2 units down. If the original parallelogram has vertices at (3, 4), (5, 4), (3, 6), and (5, 6), what are the coordinates of the new parallelogram?

• [[-1, 2], [1, 2], [-1, 4], [1, 4]]

• [[0, 2], [2, 2], [0, 4], [2, 4]]

• [[-1, 6], [1, 6], [-1, 8], [1, 8]]

• [[3, 4], [5, 4], [3, 6], [5, 6]]

A point (x, y) is reflected over the x-axis. If the original point is (-3, 5), what are the coordinates of the reflected point?

• (-3, -5)

• (-3, 0)

• (-3, 5)

• (3, 5)