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Transformations and Congruence Practice Tests

These Grade 8 Math practice tests cover translations, reflections, rotations, dilations, coordinate rules, compositions, and congruent figures.

Skills covered

  • Applying coordinate rules for translations, reflections, and rotations
  • Recognizing rigid transformations and identifying preserved measurements
  • Using compositions of transformations
  • Determining whether figures are congruent or similar
  • Connecting transformations with logos, maps, tiles, designs, and scale drawings

How to use these practice tests

Write the coordinate rule before moving each point. Then compare corresponding side lengths and angle measures to decide whether the transformation preserves congruence.

For more Grade 8 Math practice, return to the Grade 8 Math category.

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Grade 8 Transformations and Congruence Practice Tests

Practice Grade 8 Math questions about translations, reflections, rotations, dilations, coordinate rules, compositions, and congruent figures.

Choose the best answer for each question. Apply the coordinate rule carefully and decide whether lengths and angles are preserved.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A point (2,3)(2,3) is reflected across the x-axis and then translated by (1,4)(1,4). What is the final image?

Please select an answer first.

Correct answer: A

The correct answer is (3,1)(3,1).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Reflect first: (2,3)mapsto(2,−3)(2,3)\\mapsto(2,-3). Then translate: (2+1,−3+4)=(3,1)(2+1,-3+4)=(3,1).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Reflect first: (2,3)mapsto(2,−3)(2,3)\\mapsto(2,-3). Then translate: (2+1,−3+4)=(3,1)(2+1,-3+4)=(3,1).

2. QuestionMultiple choice

A point (1,−2)(1,-2) is rotated 180 degrees and then translated by (2,1)(2,1). What is the final image?

Please select an answer first.

Correct answer: B

The correct answer is (1,3)(1,3).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Rotate to (−1,2)(-1,2), then add (2,1)(2,1) to get (1,3)(1,3).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Rotate to (−1,2)(-1,2), then add (2,1)(2,1) to get (1,3)(1,3).

3. QuestionMultiple choice

A point is translated by (3,−1)(3,-1) and then by (−2,4)(-2,4). What is the net translation?

Please select an answer first.

Correct answer: C

The correct answer is (1,3)(1,3).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Add the translation vectors: (3,−1)+(−2,4)=(1,3)(3,-1)+(-2,4)=(1,3).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Add the translation vectors: (3,−1)+(−2,4)=(1,3)(3,-1)+(-2,4)=(1,3).

4. QuestionMultiple choice

A point (−3,2)(-3,2) is reflected across the y-axis and then the x-axis. What is its image?

Please select an answer first.

Correct answer: D

The correct answer is (3,−2)(3,-2).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: The y-axis reflection gives (3,2)(3,2), and the x-axis reflection gives (3,−2)(3,-2).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

The y-axis reflection gives (3,2)(3,2), and the x-axis reflection gives (3,−2)(3,-2).

5. QuestionMultiple choice

What single transformation is equivalent to reflecting a figure across both coordinate axes?

Please select an answer first.

Correct answer: A

The correct answer is A 180-degree rotation about the origin.

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Changing both coordinate signs is exactly the rule for a 180-degree rotation.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Changing both coordinate signs is exactly the rule for a 180-degree rotation.

6. QuestionMultiple choice

What does a translation do to the orientation of a figure?

Please select an answer first.

Correct answer: B

The correct answer is It preserves the orientation..

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: A translation slides the figure without flipping or turning it.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

A translation slides the figure without flipping or turning it.

7. QuestionMultiple choice

Two successive 90-degree counterclockwise rotations about the origin equal which transformation?

Please select an answer first.

Correct answer: C

The correct answer is A 180-degree rotation.

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Two quarter-turns make a half-turn, which is a 180-degree rotation.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Two quarter-turns make a half-turn, which is a 180-degree rotation.

8. QuestionMultiple choice

What is the result of reflecting a figure across y=xy=x twice?

Please select an answer first.

Correct answer: D

The correct answer is The original figure.

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Applying the same reflection twice returns every point to its original location.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Applying the same reflection twice returns every point to its original location.

9. QuestionMultiple choice

The point (3,1)(3,1) is translated by (x,y)mapsto(x−2,y+5)(x,y)\\mapsto(x-2,y+5) and then reflected across the x-axis. What is the image?

Please select an answer first.

Correct answer: A

The correct answer is (1,−6)(1,-6).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Translate to (1,6)(1,6), then reflect across the x-axis to get (1,−6)(1,-6).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Translate to (1,6)(1,6), then reflect across the x-axis to get (1,−6)(1,-6).

10. QuestionMultiple choice

A sequence of translations, reflections, and rotations is applied to a polygon. What can be said about the final polygon?

Please select an answer first.

Correct answer: B

The correct answer is It is congruent to the original polygon..

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: All three are rigid transformations and preserve side lengths and angle measures.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

All three are rigid transformations and preserve side lengths and angle measures.

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