Similarity and Similarity Transformations

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).

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.

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 would be the coordinates of the new image after the following sequence of transformations is applied to Point B(3, 2):
1. Dilate by a scale factor of 3 from the origin
2. Translate 3 units down

• B''(9, -1)

• B''(9, 6)

• B''(9, 3)

• B''(6, 6)

• B''(6, 3)

Answer explanation

B(3, 2):

1. Dilate by a scale factor of 3 from the origin (multiply the coordinates by 3) B'(9,6)

2. Translate 3 units down (subtract 3 from the y-coordinate) B''(9,3)

Choose all statements that are true.

• Dilations never increase the length of line segments.

• Dilations of a triangle are similar to the original triangle.

• Similar figures are always congruent.

• Congruent figures are always similar.

Answer explanation

Dilations can increase or decrease the length of line segments, depending on the scale factor.

Dilations of a triangle are similar to the original triangle.

Similar figures are only congruent if the side lengths are equal.

Congruent figures are always similar, because the corresponding angles are congruent.

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.

Are these triangles similar?

• Yes

• No

• 20

• 30

• 25

• 23

The pair of figures is similar. Find the missing side.

• x = 10

• x = 4

• x = 2

• x = 5