Transformations Review NYS Questions

Triangle ABC and its congruent image, triangle A'B'C', are graphed on the coordinate plane shown below. Which sequence of transformations maps triangle ABC onto triangle A'B'C'?

• A reflection over the y-axis and then a translation 2 units up

• A reflection over the y-axis and then a translation 2 units down

• A reflection over the y-axis and then a translation 8 units left

• A reflection over the y-axis and then a translation 8 units right

Triangle P undergoes a sequence of transformations resulting in triangle Q. Which sequence of transformations could be used to show that triangle Q is similar but not congruent to triangle P?

• A reflection followed by a translation

• A rotation followed by a reflection

• A reflection followed by a rotation

• A translation followed by a dilation

Triangle QPR is graphed on the coordinate plane below. Triangle QPR is dilated by a scale factor of 1/2 with a center of dilation at the origin, resulting in triangle Q'P'R'. What are the coordinates of vertex R'?

• (2,5)

• (5,2)

• (8,20)

• (20,8)

On a coordinate plane, vertex A for triangle ABC is located at (6, 4). Triangle ABC is dilated by a scale factor of 0.5 with the center of dilation at the origin. The resulting image is triangle A'B'C'. What are the coordinates of vertex A'?

• (3, 2)

• (12, 8)

• (5.5, 3.5)

• (6.5, 4.5)

Triangle F and triangle G are shown below. Which sequence does not transform triangle F to triangle G?

• A 180° clockwise rotation about the origin

• B 180° counterclockwise rotation about the origin

• C a reflection over the x-axis and then a reflection over the y-axis

• D a reflection over the y-axis and then a 90° clockwise rotation about the origin

A parallelogram with vertices at (0, 3), (2, 0), (4, 2), and (2, 5) is reflected over the y-axis. Which vertex of the parallelogram will have the same x-coordinate before and after the reflection?

• A (0, 3)

• B (2, 0)

• C (4, 2)

• D (2, 5)

The vertices of a triangle are located at F(−4, −2), G(2, 2), and H(0, −4). A sequence of transformations to triangle FGH results in triangle F'G'H', as shown below. Which sequence of transformations to triangle FGH results in triangle F'G'H'?

• A 90° clockwise rotation about the origin, then a dilation by a scale factor of 2 with a center of dilation at the origin

• A 90° counterclockwise rotation about the origin, then a dilation by a scale factor of 2 with a center of dilation at the origin

• A 90° counterclockwise rotation about the origin, then a dilation by a scale factor of 1/2 with a center of dilation at the origin

• A 90° clockwise rotation about the origin, then a dilation by a scale factor of 1/2 with a center of dilation at the origin

Quadrilateral ABCD is graphed on a coordinate plane, with point C plotted at (−4,3). Quadrilateral ABCD is then reflected over the y-axis to create its image A'B'C'D'. After the reflection, what are the coordinates of point C'?

• (4, 3)

• (4, −3)

• (−4, 3)

• (−4, −3)

Lily wants to define a transformation (or series of transformations) using only rotations, reflections, or translations that takes Figure A to Figure B. Which statement about the transformation that Lily wants to define is true?

• It can be defined with two reflections.

• It can be defined with one rotation and one translation.

• It cannot be defined because Figure A and Figure B are not congruent.

• It cannot be defined because the longest side of Figure B is on the bottom.

Acute ΔABC is rotated about a point and then dilated by a scale factor of 1/2 to produce ΔA'B'C'. Which statement correctly compares ΔA'B'C' to ΔABC?

• The angle measures and the side lengths of ΔA'B'C' are are half the size of those of ΔABC.

• The angle measures of ΔA'B'C' are the same as those of ΔABC, but the side lengths of ΔA'B'C' are half the size of those of ΔABC.

• 
  The angle measures of ΔA'B'C' are the same as those of ΔABC, but the side lengths of ΔA'B'C' are twice the size of those of ΔABC.

  
  

• The angle measures of ΔA'B'C' depend on the angle of rotation, but the side lengths of ΔA'B'C' are half the size of those of ΔABC.