AnswersSRC 2022 MJ Grade 8 Pre-Algebra Q1Congruence and Transformations

Congruence and Transformations Answers

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Triangle GHI is rotated 90 clockwise and then reflected over the y-axis. Which congruency statement is true?

Question illustration
A
Angle G is congruent to angle H is congruent to angle I
Option A
B
Angle G double-prime is congruent to angle H double-prime is congruent to angle I double-prime
Option B
C
Triangle G H I is congruent to triangle G double-prime H double-prime I double-prime
Option C
D
Triangle G H I is congruent to triangle I H G
Option D
3

Alexi transformed figure L such that its image is figure K after a 90 counterclockwise rotation about the origin and a reflection over the y-axis. Jonathan used figure L to perform the same transformation, but he reflected figure L over the y-axis before performing the 90 counterclockwise rotation. Which best compares Alexi’s and Jonathan’s transformed figures?

Question illustration
A
The change in order will not affect the final image. Their transformed figures will be identical.
B
The change in order will result in the transformed images having vertices in the same location, but in a different orientation.
C
The change in order will result in the transformed image of figure L being transformed back onto figure L.
D
The change in order will result in the transformed image of figure L having a different location.
4

Chareese reflects figure RSUT over the y-axis and then rotates the reflected figure 180 about the origin, resulting in figure A. She states that . Which best describes the accuracy of her congruency statement?

Question illustration
A
Accurate. A reflection will change the direction the vertices trace around the figure. A rotation preserves the change.
B
Accurate. A reflection preserves the direction the vertices trace around the figure. A rotation changes that direction.
C
Inaccurate. The correct congruency statement is .
Option C
D
Inaccurate. The correct congruency statement is .
Option D
5

Triangle RST is translated 2 units left and then reflected over the y-axis. Which transformations of RST will result in the same image? Check all that apply.

Question illustration
A
a reflection over the y-axis and then a translation 2 units right
B
a 180 rotation about the origin, then a translation 2 units right, and then a reflection over the x-axis
Option B
C
a reflection over the y-axis and then a translation 2 units left
D
a 180 rotation about the origin, then a translation 2 units left, and then a reflection over the x-axis
Option D
E
a reflection over the x-axis and then a translation 2 units right
F
a reflection over the x-axis and then a translation 2 units left
6

Triangle MNO is rotated 180 using the origin as the center of rotation. Which sequences of transformations will produce the same results? Check all that apply.

Question illustration
A
a reflection over the x-axis and then a reflection over the y-axis
B
a reflection over the y-axis and then a reflection over the x-axis
C
a 90 clockwise rotation about the origin and then a 90 counterclockwise rotation about the origin
Option C
D
a translation 6 units right and then a reflection over the x-axis
E
a translation 4 units down and then a reflection over the y-axis
8

Which sequence of transformations produces A’B’C’ from ABC?

Question illustration
A
a translation up 3 and then a 90º counterclockwise rotation about the origin
B
a 90º counterclockwise rotation about the origin and then a translation up 3
C
a reflection over the x-axis and then a translation left 2 and down 1
D
a translation left 5 and down 2 and then a reflection over the x-axis
9

Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?

Question illustration
A
Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
B
Translate the pre-image up 3 and right 4 and then reflect the figure over the x-axis.
C
Translate the pre-image up 4 and left 3 and then reflect the figure over the y-axis.
D
Translate the pre-image down 3 and right 4 and then reflect the figure over the x-axis.
10

Mrs. Hamilton shows her students this graph and asks them to determine how figure A was transformed to figure B. .Marcus suggests that figure A was reflected over the y-axis and then translated 2 to the right and 1 up. Julianne agrees, and states that the transformations could happen in any order. Which best describes the accuracy of Julianne’s statement?

Question illustration
A
Accurate. A translation of figure A of 2 to the right and 1 up and then a reflection over the y-axis produces the image, figure B.
B
Accurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right produces the image, figure B.
C
Inaccurate. A translation of 2 to the right and 1 up and then a reflection over the y-axis results in a figure that is located in the second quadrant.
D
Inaccurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right results in a figure that is located in the second quadrant.

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