Rigid Transformations

If a point (3, 4) is translated 5 units right and 2 units down, what are the coordinates of the new point?

• (8, 2)

• (8, 6)

• (2, 6)

• (2, 2)

A triangle with vertices at (1, 2), (4, 2), and (1, 5) is rotated 90 degrees counterclockwise about the origin. What are the coordinates of the new vertices?

• (-2, 1), (-2, 4), (-5, 1)

• (2, -1), (2, -4), (5, -1)

• (-2, -1), (-2, -4), (-5, -1)

• (2, 1), (2, 4), (5, 1)

What is the result of reflecting the point (5, -3) across the y-axis?

• (-5, 3)

• (5, 3)

• (-5, -3)

• (5, -3)

A rectangle is reflected over the line y = x. If one of the original vertices of the rectangle is at (3, 7), where is the corresponding vertex after the reflection?

• (7, 3)

• (3, -7)

• (-7, -3)

• (-3, -7)

If a figure undergoes a rotation of 180 degrees about the origin, which of the following statements is true about the coordinates of any point (x, y) on the figure?

• The coordinates become (-x, y)

• The coordinates become (x, -y)

• The coordinates become (-x, -y)

• The coordinates remain (x, y)

What is the image of the point (2, -4) after a translation of 3 units to the left and 6 units up?

• (-1, 2)

• (5, 2)

• (5, -10)

• (-1, -10)

A figure is rotated 90 degrees clockwise about the point (1, 1). If a point on the figure is at (2, 3) before the rotation, what is its position after the rotation?

• (3, 0)

• (0, 2)

• (-1, 3)

• (3, 2)

Which of the following transformations would map the point (x, y) onto the point (y, -x)?

• Reflection over the x-axis followed by a translation

• Rotation of 90 degrees counterclockwise about the origin

• Reflection over the line y = x

• Rotation of 90 degrees clockwise about the origin

What is the result of reflecting the point (7, -2) across the x-axis?

• (7, 2)

• (-7, -2)

• (-7, 2)

• (7, -2)

If a point (6, 8) is translated 4 units left and 3 units up, what are the coordinates of the new point?

• (2, 11)

• (10, 11)

• (2, 5)

• (10, 5)