Mastering Transformations: Reflections, Rotations, and More

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

• A'(-1, 2), B'(-3, 4), C'(-5, 2)

• A'(1, 2), B'(3, 4), C'(5, 2)

• A'(-1, 4), B'(-3, 2), C'(-5, 4)

• A'(-1, -2), B'(-3, -4), C'(-5, -2)

A rectangle has corners at (2, 3), (2, 7), (6, 3), and (6, 7). If the rectangle is translated 4 units to the right and 2 units up, what are the new coordinates of the corners?

• [(2, 5), (2, 9), (6, 5), (6, 9)]

• [(6, 5), (6, 9), (10, 5), (10, 9)]

• [(2, 3), (2, 7), (6, 3), (6, 7)]

• [(6, 3), (6, 7), (10, 3), (10, 7)]

A square is rotated 90 degrees clockwise around the origin. If one vertex of the square is at (2, 1), what are the coordinates of that vertex after the rotation?

• (-1, 2)

• (1, -2)

• (0, 2)

• (2, 1)

A point P(4, -3) is dilated from the origin by a scale factor of 2. What are the coordinates of point P after the dilation?

• (6, -4)

• (8, -6)

• (4, -6)

• (8, 3)

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

• (1, 1), (4, 1), (3, 2), (2, 2)

• [(1, 1), (1, 4), (3, 3), (3, 2)]

• (1, 4), (4, 4), (3, 3), (2, 3)

• (1, 1), (4, 3), (3, 1), (2, 1)

A circle with center at (0, 0) and radius 5 is translated 3 units left and 2 units down. What is the new center of the circle?

• (-3, -2)

• (-5, 0)

• (3, 2)

• (0, -5)

A pentagon has vertices at (1, 1), (2, 3), (3, 1), (4, 3), and (2.5, 4). If the pentagon is rotated 180 degrees around the point (2.5, 2), what are the new coordinates of the vertices?

• [(4, 1), (3, 3), (2, 1), (1, 3), (2.5, 6)]

• [(4, 3), (3, 1), (2, 3), (1, 1), (2.5, 0)]

• [(1, 3), (2, 1), (3, 3), (4, 1), (2.5, 2)]

• [(2, 1), (3, 3), (4, 1), (5, 3), (2.5, 5)]

A figure is scaled by a factor of 0.5. If the original dimensions of the figure are 10 cm by 8 cm, what will be the new dimensions after scaling?

• 6 cm by 4 cm

• 5 cm by 4 cm

• 5 cm by 5 cm

• 10 cm by 8 cm

A line segment connects points A(2, 3) and B(4, 7). If the segment is reflected over the x-axis, what are the coordinates of the endpoints after the reflection?

• A'(-2, 3), B'(-4, 7)

• A'(2, -3), B'(4, -7)

• A'(2, 3), B'(4, 7)

• A'(2, -7), B'(4, -3)

A rectangle is defined by the points (1, 1), (1, 4), (5, 1), and (5, 4). If the rectangle is rotated 270 degrees counterclockwise around the origin, what are the new coordinates of the corners?

• [(1, -1), (4, -1), (1, -5), (4, -5)]

• (1, 1), (1, 5), (5, 1), (5, 5)

• (1, 1), (4, 1), (1, 4), (4, 4)

• (1, -4), (4, -4), (1, -1), (4, -1)