Triangle ABC is rotated 180º using the origin as the center of rotation. Which sequence of transformations will produce the same result?

a reflection over the x -axis and then a reflection over the y -axis

a translation up 4 and then a reflection over the y -axis

a translation up 4 and then a translation right 6

a translation right 6 and then a reflection over the x -axis

Figure X is translated down 5 and then reflected over the y -axis, forming figure Y . Which sequence of transformations results in the same transformation?

a reflection over the y -axis and then a translation down 5 units

a translation left 5 units and then a reflection over the x -axis

a translation left 5 units and then a translation down 5 units

a 180 degree rotation using the origin as the center of rotation

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

a translation up 3 and then a 90º counterclockwise rotation about the origin

a 90º counterclockwise rotation about the origin and then a translation up 3

a reflection over the x -axis and then a translation left 2 and down 1

a translation left 5 and down 2 and then a reflection over the x -axis

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?

Translate the pre-image down 4 and right 3 and then reflect the figure over the x -axis.

Translate the pre-image up 3 and right 4 and then reflect the figure over the x -axis.

Translate the pre-image up 4 and left 3 and then reflect the figure over the y -axis.

Translate the pre-image down 3 and right 4 and then reflect the figure over the x -axis.

The vertices A (–2, –1), B (–3, 2), C (–1, 3), and D (0, 0) form a parallelogram. The vertices A ’(–1, –2), B ’(2, –3), C ’(3, –1), and D ’(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?

a reflection over the y -axis and then a 90 degree clockwise rotation about the origin

a reflection over the x -axis and then a reflection over the y -axis

a 90 degree clockwise rotation about the origin and then a reflection over the y -axis

a 90 degree counterclockwise rotation about the origin and then a reflection over the x -axis

Which sequence of transformations produces R’S’T’ from RST ?

a translation 2 units right and then a reflection over the x -axis

a 90 degree clockwise rotation about the origin and then a translation 2 units left

a 90 degree counterclockwise rotation about the origin and then a translation 2 units right

a translation 2 units left and then a reflection over the y -axis

$$\Delta ABC\cong\Delta RST\ \ \ $$ $$\Delta ABC\cong\Delta TSR$$ Which best describes the accuracy of the congruency statements?

Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC.

Jason’s statement is correct. RST is the same orientation, shape, and size as ABC.

Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a rotation and a translation of ABC.

Kelley’s statement is correct. TSR is the same orientation, shape, and size as ABC.

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?

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.

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 .

Accurate. A reflection over the y -axis and then a translation of 1 up and 2 to the right produces the image, figure B .

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.

A teacher asks students to determine the accuracy of this statement. A reflection over the x -axis and then over the y -axis results in the same transformation as a 180 rotation about the origin of the original figure. Kwame’s explanation of the accuracy of the statement is shown below. Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3). Step 2: Reflect the pre-image over the x -axis: (1, –2), (1, –4), (2, –3). Step 3: Reflect the figure from step 2 over the y -axis: (–1, 2), (–1, 4), (–2, 3). Step 4: Rotate the pre-image 180: (–1, –2), (–1, –4), (–2, –3). Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate. Which best explains Kwame’s solution?

Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.

Kwame’s explanation and solution are incorrect. He reflected the image over the y- axis in step 2 and the x- axis in step 3, instead of the reverse.

Kwame’s explanation and solution are incorrect. When reflecting over the x- and y -axes, he negated the incorrect coordinate in the ordered pair.

Kwame’s explanation and solution are incorrect. The coordinates of the rotated figure should be switched and negated, not just negated.

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?

The change in order will result in the transformed image of figure L having a different location.

The change in order will not affect the final image. Their transformed figures will be identical.

The change in order will result in the transformed images having vertices in the same location, but in a different orientation.

The change in order will result in the transformed image of figure L being transformed back onto figure L .

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

a reflection over the x -axis and then a reflection over the y -axis

a 90 degree clockwise rotation about the origin and then a 90 degree counterclockwise rotation about the origin

a translation 6 units right and then a reflection over the x -axis

a translation 4 units down and then a reflection over the y -axis

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.

a reflection over the y- axis and then a translation 2 units right

a 180 degree rotation about the origin, then a translation 2 units right, and then a reflection over the x -axis

a reflection over the y -axis and then a translation 2 units left

a 180 degree rotation about the origin, then a translation 2 units left, and then a reflection over the x -axis

a reflection over the x -axis and then a translation 2 units right

Congruence and Transformations

Authored by Barbara White

Mathematics

8th Grade

CCSS covered

Used 24+ times

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20 questions

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

Each triangle is a right triangle.

Each triangle is an isosceles triangle.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

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

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

The triangles are equilateral.

The triangles are right triangles.

Triangles X and Z are congruent.

Triangles X, Y, and Z share one or more vertices.

Tags

CCSS.8.G.A.2

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Triangle ABC is shown with four images that are each the result of a transformation of triangle ABC.

For which triangle is one reflection necessary for the transformation to occur?

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

FGHI

JKLM

NOPQ

RSTU

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H.

Which sequence of transformations will produce the same results?

a reflection over the y-axis and then a rotation 90 degrees clockwise about the origin

a reflection over the x-axis and then a rotation 90 degrees clockwise about the origin

a 180 degree rotation about the origin

a reflection over the y-axis and then a reflection over the x-axis

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Harley graphs a polygon that is located entirely inside quadrant I. He rotates the figure clockwise 90 degrees about the origin and then reflects the rotated figure over the x-axis. He translates the resulting figure 3 units to the left and 3 units up. Which best describes the location of the final image?

quadrant I

quadrant II

above the x-axis

left of the y-axis

Tags

CCSS.8.G.A.3

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Congruence and Transformations

Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

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

Triangle ABC is shown with four images that are each the result of a transformation of triangle ABC.

For which triangle is one reflection necessary for the transformation to occur?

Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H.

Which sequence of transformations will produce the same results?

Triangle ABC is rotated 180º using the origin as the center of rotation.
Which sequence of transformations will produce the same result?

Figure X is translated down 5 and then reflected over the y-axis, forming figure Y.
Which sequence of transformations results in the same transformation?

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

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Similar Resources on Wayground

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Discover more resources for Mathematics

Congruence and Transformations

Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

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

Triangle ABC is shown with four images that are each the result of a transformation of triangle ABC.For which triangle is one reflection necessary for the transformation to occur?

Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H.Which sequence of transformations will produce the same results?

Triangle ABC is rotated 180º using the origin as the center of rotation.Which sequence of transformations will produce the same result?

Figure X is translated down 5 and then reflected over the y-axis, forming figure Y.Which sequence of transformations results in the same transformation?

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

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Triangle ABC is shown with four images that are each the result of a transformation of triangle ABC.

For which triangle is one reflection necessary for the transformation to occur?

Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H.

Which sequence of transformations will produce the same results?

Triangle ABC is rotated 180º using the origin as the center of rotation.
Which sequence of transformations will produce the same result?

Figure X is translated down 5 and then reflected over the y-axis, forming figure Y.
Which sequence of transformations results in the same transformation?