Congruent and Similar Figures Transformations

What is the sequence of transformations?

• Reflect over the y-axis then reflect over the x-axis

• Reflect over the x-axis then reflect over the y-axis

• Translate 4 units then rotate 90˚

• Rotate 90˚ then reflect over the x-axis

Choose the correct transformations

• rotate 90 degrees counter-clockwise around the origin, and then reflect over the x-axis

• right 1, down 4, and then reflection over the y-axis

• right 6, and then reflection over the x-axis

• reflection over the line y=x, and then translate up 4, right 2

Which series of transformations were performed in the figure?

• Translation 5 units down, reflection over the y-axis

• Reflection over the x-axis, translation 6 units right

• Rotation 90^o clockwise, reflection over the x-axis

• Rotation 180^o clockwise, reflection over the y-axis

Rectangle ABCD is undergoing a series of transformations. Which of the following transformations will NOT cause the resulting rectangle to maintain congruence with rectangle ABCD?

• Translation 3 units left, then translation 7 units down.
  

• Dilation by a scale factor of 3, then dilation by a scale factor of 3.

• Dilation by a scale factor of 2, then dilation by a scale factor of 1/2.

• Translation 4 units right, then translation 6 units up. 

Which transformation(s) preserve congruency? (Choose all that apply)

• rotations

• reflections

• translations

• dilations

If the scale factor is less than one, the new figure will be

• an enlargement

• a reduction

• a scale factor

• bigger

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)

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).

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)