Congruence Sequences of Transformations

rotation 90° counterclockwise about the origin, then reflect over x-axis.

• R(-4.5, 4.5)

• R(3, -3)

• R(-5, 2)

• R(-3, 3)

Are these two polygons congruent?

• yes

• no

• maybe

• Translation

• Reflection

• Rotation

• Dilation

• a single reflection

• a single rotation

• a single translation

• a translation, then a reflection

• a reflection, then a different reflection

• Pair 1

• Pair 2

• Pair 3

• Pair 4

• Because it's not the same size

• Because it's not the same shape

• Because it's a reflection over point P

• Because it's a translation

Which of these sequences of transformations would not return a shape to its original position?

• Translate 3 units up, then 3 units down

• Reflect over line p, then reflect over line p again

• Translate 1 unit to the right, then 4 units to the left, then 3 units to the right

• Rotate 120 degrees counterclockwise around Center C, then rotate 220 degrees counterclockwise around C again.

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

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 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.