Mastering Rigid Motions: Transformations in Geometry

A triangle is rotated 90 degrees clockwise around the origin. If the original triangle has vertices at (1, 2), (3, 4), and (5, 1), what are the coordinates of the new triangle?

• [(1, 2), (3, 4), (5, 1)]

• [(2, -1), (4, -3), (1, -5)]

• [(2, 1), (4, 3), (1, 5)]

• [(0, 1), (2, 3), (4, 0)]

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

• (3, 2), (5, 2), (5, 4), (3, 4)

• (-2, -3), (-2, -5), (-4, -5), (-4, -3)

• [(-2, 3), (-2, 5), (-4, 5), (-4, 3)]

• (2, 3), (2, 5), (4, 5), (4, 3)

A square is translated 3 units to the right and 2 units down. If the original square has vertices at (1, 1), (1, 3), (3, 3), and (3, 1), what are the coordinates of the translated square?

• [(1, -1), (1, 1), (3, 1), (3, -1)]

• [(3, 3), (3, 5), (5, 5), (5, 3)]

• [(4, 1), (4, 3), (6, 3), (6, 1)]

• [(4, -1), (4, 1), (6, 1), (6, -1)]

A pentagon is dilated from a point (0, 0) by a scale factor of 2. If one vertex of the pentagon is at (2, 3), what will be the new coordinates of that vertex after dilation?

• (6, 9)

• (2, 3)

• (1, 1)

• (4, 6)

A figure is rotated 180 degrees about the point (2, 2). If one vertex of the figure is at (4, 5), what will be the new coordinates of that vertex?

• (6, 7)

• (0, -1)

• (4, 5)

• (2, 2)

A triangle is translated left by 4 units and up by 3 units. If the original triangle has vertices at (5, 6), (7, 8), and (9, 6), what are the coordinates of the new triangle?

• [(5, 6), (7, 8), (9, 6)]

• [(1, 9), (3, 11), (5, 9)]

• [(2, 8), (4, 10), (6, 8)]

• [(1, 3), (3, 5), (5, 3)]

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

• [(2, 3), (1, 4), (5, 1), (4, 5)]

• [(1, 2), (3, 1), (4, 5), (2, 4)]

• [(3, 4), (1, 2), (4, 2), (5, 3)]

• [(2, 1), (1, 3), (5, 4), (4, 2)]

A circle is translated 5 units to the left. If the center of the original circle is at (6, 7), where is the center of the translated circle?

• (6, 7)

• (1, 12)

• (1, 7)

• (11, 7)

A triangle undergoes a sequence of transformations: first a reflection over the x-axis, then a translation 2 units up. If the original triangle has vertices at (1, 1), (2, 3), and (3, 1), what are the coordinates of the final triangle?

• (1, -1), (2, -1), (3, -1)

• (1, 3), (2, 1), (3, 3)

• [(1, 1), (2, -1), (3, 1)]

• (1, 1), (2, 3), (3, 1)

A hexagon is rotated 120 degrees counterclockwise about its center. If one vertex of the hexagon is at (3, 0), what will be the new coordinates of that vertex after the rotation?

• (3, 0)

• (1.5, -2.598)

• (-1.5, 2.598)

• (0, 3)