Congruent Figures and Sequences of Transformations

What sequence of transformations will get you from figure 1 to figure 3?

• reflection, then rotation

• rotation, then translation

• reflection, then translation

• Translation, then reflection

Which transformation would be used on quadrilateral KLMN to create quadrilateral K'L'M'N' ?

• rotation 90˚ clockwise around the origin

• reflection across the x-axis

• translation to the right

• reflection across the y-axis

• (-4, 4)

• (-4, 1)

• (4, -4)

• (4, -1)

Define congruent figures

• two figures that are the same shape

• two figures that are the same size and the same shape

• two figures that are the same size

• two figures that are both rectangles

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

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).

The preimage above is rotated 90^o counterclockwise. How do the side lengths in the preimage compare to the side lengths in the image?

• Some of the side lengths increase in measure and other side lengths decrease in measure.

• The measures of the side lengths double.

• The measures of the side lengths decrease by one third.

• The measures of the side lengths are the same.

Answer explanation

A rotation is a rigid transformation, which means size is unchanged when applied. That means the side lengths are the same.

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).

Which transformation will map an image onto itself?

• A translation 3 units right and 3 units up

• A rotation 360^o clockwise

• A reflection over the y-axis followed by a translation 3 units down

• A dilation followed by a 90^o clockwise rotation

Answer explanation

A 360 degree rotation is a full rotation, which means. the figure ends up where it started.