Unit 6 (Congruence & Similarity through Transformations)

Which picture shows a TRANSLATION?

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Answer explanation

A translation does not change the orientation of a figure.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

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).

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

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.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

Which of the following images shows a rotation of 180^o?

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Answer explanation

A 180 degree rotation is half of a full rotation, so it will result in a figure being rotated upside down and in the opposite quadrant of the graph.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

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.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

Point A(-6, 5) is rotated 90 degrees clockwise.

The image of Point A, Point A' is in which Quadrant?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Answer explanation

Point A(-6, 5) is in Quadrant II. A 90 clockwise rotation goes the opposite direction of the quadrant numbering scheme, so the new image will be in Quadrant I.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.3

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

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3

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)

Tags

CCSS.8.G.A.3

CCSS.8.G.A.4

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)

Tags

CCSS.8.G.A.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.

Tags

CCSS.8.G.A.1

CCSS.8.G.A.2

CCSS.8.G.A.3