Nonrigid Geometric Transformations

Which transformations below will always produce an image that is congruent to the original figure? Select all that apply.

• Translation

• Dilation

• Rotation

• Reflection

• reflect over x-axis

• reflect over y-axis

• reflect x = 4

• reflect x = -4

• reflection y = x

The figure below shows line segments a and b passing through a regular pentagon. Which statement describes a series of transformations that will result in a pentagon that is mapped onto the one shown?

• rotating the pentagon 72° clockwise about its center and then reflecting it across segment a

• rotating the pentagon 72° clockwise about its center and then reflecting it across segment b

• rotating the pentagon 90° clockwise about its center and then reflecting it across segment a

• rotating the pentagon 90° clockwise about its center and then reflecting it across segment b

Which figure always has exactly four lines of reflection that map the figure onto itself?

• Square

• Rectangle

• Regular Octagon

• Equilateral Triangle

Which sequence of two transformations will map ∆MNP onto ∆QRS?

• Reflection across the y-axis followed by 90° counterclockwise rotation around the origin

• Reflection across the x-axis followed by reflection across the y-axis

• 180° rotation

• 270° counterclockwise rotation about the origin followed by translation 5 units left

Which sequence of transformations will map ∆ABC onto ∆DEF? Select all that apply.

• Reflection across the line y = x

• Reflection across the x-axis followed by 90° rotation about the origin.

• Reflection across the x-axis followed by reflection across the y-axis.

• 180° rotation about the origin

The graph shows ∆ABC and ∆A’B’C’.

Given Quadrilateral PQRS with coordinates and which of the following transformations will result in the image of the quadrilateral being located only in the first quadrant of the coordinate plane? Select each correct answer.

• A translation right 4 units

• A reflection across x = 4

• A reflection across y = -x

• A reflection across x = 3, followed by a translation up 8 units

Which sequence of transformations will result in an image that is NOT congruent to graphed on the coordinate grid below?

• a translation 4 units to the left followed by a reflection across the x-axis

• a reflection across the y-axis followed by a rotation 90° clockwise about the origin

• a dilation by a scale factor of 2 about the origin, followed by a translation 3 units down

• a rotation 90° clockwise about the origin followed by a dilation by a scale factor of 1 about the origin