Sequence of Transformations to Identify Similar Figures

Rectangle A’B’C’D’ is similar to rectangle ABCD, as shown on the coordinate plane in the picture. Which sequence of transformations maps rectangle ABCD onto rectangle A’B’C’D’ ?

• a translation 8 units to the left, then a dilation by a scale factor of 1/2 with a center of dilation at the origin

• a reflection over the y axis, then a dilation by a scale factor of 1/2 with a center of dilation at the origin

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

Which sequence of transformations takes Δ A to its image, Δ B?

• reflection over the x-axis and translation 2 units down

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

• translation 2 units down and 90° rotation about the origin

• translation 12 units right and 90° rotation about the origin

A sequence of transformations was applied to an equilateral triangle in a coordinate plane. The transformations used were rotations, reflections, and translations. Which statement about the resulting figure is true?

• It must be an equilateral triangle with the same side lengths as the original triangle

• It must be an equilateral triangle, but the side lengths may differ from the original triangle.

• It may be a scalene triangle, and all the side lengths may differ from the original triangle.

• It may be an obtuse triangle with at least one side the same length as the original triangle

Figure Q was the result of a sequence of transformations on figure P, both shown in the picture. Which sequence of transformations could take figure P to figure Q?

• reflection over the x-axis and translation 7 units right

• reflection over the y-axis and translation 3 units down

• translation 1 unit right and 180° rotation about the origin

• translation 4 units right and 180° rotation about the origin

Figure X and figure Y are shown on the coordinate grid below. Which statement about figures X and Y must be true?

• A series of translations will transform figure X to figure Y, and the figures will be congruent.

• A 180° clockwise rotation will transform figure X to figure Y, and the figures will be congruent.

• A series of translations will transform figure X to figure Y, but the figures will not be congruent.

• A 180° clockwise rotation will transform figure X to figure Y, but the figures will not be congruent.

Figure L and figure M are shown on the grid in the picture. Luis wants to transform figure L to figure M using only rotations, reflections, and translations. Which statement is true?

• The transformation can be done with a reflection followed by a rotation.

• The transformation can be done with a reflection followed by a translation.

• The transformation cannot be done because figure L is not congruent to figure M.

• The transformation cannot be done because figures L and M are in different quadrants.

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

• a 180° clockwise rotation about the origin

• a 180° counterclockwise rotation about the origin

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

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

Squares PQRS and TUVW are shown in the picture. Which sequence of transformations of square PQRS shows that square PQRS is congruent to square TUVW?

• a translation 2 units up and 2 units to the right, then a reflection over the x-axis

• a translation 2 units up and 2 units to the right, then a reflection over the y-axis

• a translation 2 units down and 2 units to the left, then a reflection over the x-axis

• a translation 2 units down and 2 units to the left, then a reflection over the y-axis

Triangle A and triangle B are graphed on the coordinate plane in the picture. Which sequence of transformations will map triangle A onto its congruent image, triangle B?

• a reflection over the x axis, then a reflection over the y axis

• a translation 8 units down, then a reflection over the y axis

• a reflection over the x axis, then a translation 6 units to the left

• a rotation clockwise 90° about the origin, then a translation 6 units to the left

Two transformations are performed on a figure on a coordinate plane. The first transformation is a translation 8 units to the left. Which second transformation will result in an image that is similar to, but not congruent to, the original figure?

• a clockwise rotation of 90° about the center

• a clockwise rotation of 180° about the center

• a dilation by a scale factor of 1 with the origin as the center of dilation

• a dilation by a scale factor of ½ with the origin as the center of dilation