Sequences of Transformations and Congruent Figures

• (1, -2)

• (-1, 2)

• (-1, -2)

• (1, 2)

Which sequences make congruent figures?

• translations only

• rotations, reflections, and translations

• rotations and reflections only

• dilations, reflections, rotations, and translations

Describe the translations that were applied to quadrilateral ABCD when it was translated to quadrilateral A'B'C'D'

• down 1 unit, left 5 units

• down 4 units, left 9 units

• 5 units right, 1 unit up

• 9 units right, 4 units up

Identify the transformation of figure PQRSTU to figure P"Q"R"S"T"U"

• translation across the y-axis

• reflection across the x-axis

• reflection across the y-axis

• rotation 90˚ about the origin

• (-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)

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)

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.