Transformations, Congruence and Similarity

What will be the new position of the given point after rotating 90^o counterclockwise or 270^o clockwise?

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Answer explanation

Counterclockwise follows the numbering scheme of the quadrants. If the preimage is in the bottom left quadrant (QIII), then the new image after a 90 degree counterclockwise rotation will be in the next quadrant (QIV) in the bottom right.

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.

What would be the coordinates of the new image after the following sequence of transformations is applied to Point B(3, 2):

• 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)

In order to prove that two figures are congruent, I must show that I can map one to the other using the following transformations (select all that apply):

• Translation

• Rotation

• Reflection

• Dilation

Answer explanation

Congruent figures have the same shape AND size. This means all side lengths are equal. If a dilation is applied, that means the image and preimage are not the same size and therefore not congruent.

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 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.

Determine if the two figures are similar by using transformations.

• similar; a reflection and a dilation map one figure onto the other.

• similar; a rotation and a dilation map one figure onto the other.

• similar; a translation and a dilation map one figure onto the other.

• the figures are not similar.

The triangles are similar. Each side of ABC is 1 1/2 times longer than the sides of DEF. If the perimeter of ABC is 36cm, what is the perimeter of DEF?

• 24cm

• 54cm

• 18cm

• 12cm

The two triangles are similar. Find the distance d across the river?

• 81m

• 18m

• 16m

• 25m

The figures are similar. Find the perimeter of the second figure.

• 8ft

• 12ft

• 18ft

• 15ft