Transformations, Congruence, Similarity and Dilations

What is the scale factor that you must use to map FROG to F'R'O'G'?

Answer explanation

FROG is the larger figure and the preimage. F'R'O'G' is the smaller figure and the new image. This means the figure was dilated by a value less than 1 in order to get smaller.

The side lengths on F'R'O'G' are all half as long as those of FROG. This means FROG must have been dilated by

$\frac{1}{2}$ (or 0.5)

Choose the statement that accurately describes the relationship between ABCD and EFGH.

• ABCD and EFGH are congruent, but not similar.

• ABCD and EFGH are similar, but not congruent.

• ABCD and EFGH are both congruent and similar.

• ABCD and EFGH are neither congruent, nor similar.

Answer explanation

The figures are similar, because they have congruent corresponding angles and proportional corresponding side lengths.

They are not congruent, because they are not the same size (the corresponding side lengths are not congruent/equal).

What will be the new position of the given point after a reflection across the y-axis?

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Answer explanation

Reflecting across the y-axis flips the figure over the y-axis, so if it starts in the top left quadrant (QII), then the new image will end up in the top right quadrant (QI).

Choose all possible sequences of transformations that would map figure MATH to figure M'A'T'H'.

• Rotate 180 degrees

• Rotate 90 degrees clockwise, then reflect across the x-axis

• Rotate 90 degrees counter clockwise, then reflect across the y-axis

• Reflect over the line y=x

• None of the above

Which sequence of transformations shows that Figure 1 is congruent to Figure 2?

• Figure 2 is obtained by reflecting Figure 1 across the x-axis and then translating it 2 units right and 8 units up.

• Figure 2 is obtained by reflecting Figure 1 across the x-axis and then translating it 2 units left and 8 down.

• Figure 2 is obtained by reflecting Figure 1 across the y-axis and then translating it 2 units right and 8 units up.

• Figure 2 is obtained by reflecting Figure 1 across the y-axis and then translating it 2 units left and 8 units down.

Which of the following do not preserve congruence?

• reflections

• translations

• rotations

• dilations

Answer explanation

Dilations change size so they do not stay the same size...aka they do not preserve their size or congruence.

What is the rule for the dilation pictured below?

• (x, y) → (½x, ½y)

• (x, y) → (x + 2, y + 2)

• (x, y) → (2x, 2y)

• (x, y) → (2x, 3y)

A dilation of a figure is ___________.

• Congruent

• Similar

• Neither congruent nor similar

• Not proportional

The triangles are similar. Which series of transformations maps ABC onto DEF?

• reflection followed by a dilation

• rotation followed by a dilation

• translation followed by a dilation

• translation followed by a rotation

The triangles are similar. Which series of transformations maps ABC onto DEF?

• translation followed by a rotation

• translation followed by a dilation

• rotation followed by a dilation

• reflection followed by a dilation