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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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1. Test

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

The point (1,5)(1,5) is translated by (x,y)mapsto(x+3,y−2)(x,y)\\mapsto(x+3,y-2). What is its image?

Please select an answer first.

Correct answer: A

The correct answer is (4,3)(4,3).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Add 3 to x and subtract 2 from y: (1+3,5−2)=(4,3)(1+3,5-2)=(4,3).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Add 3 to x and subtract 2 from y: (1+3,5−2)=(4,3)(1+3,5-2)=(4,3).

2. QuestionMultiple choice

What is the reflection of (2,−3)(2,-3) across the x-axis?

Please select an answer first.

Correct answer: B

The correct answer is (2,3)(2,3).

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

A reflection across the x-axis changes (x,y)(x,y) to (x,−y)(x,-y).

3. QuestionMultiple choice

What is the reflection of (−4,1)(-4,1) across the y-axis?

Please select an answer first.

Correct answer: C

The correct answer is (4,1)(4,1).

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

A reflection across the y-axis changes (x,y)(x,y) to (−x,y)(-x,y).

4. QuestionMultiple choice

A point (2,1)(2,1) is rotated 90 degrees clockwise about the origin. What is its image?

Please select an answer first.

Correct answer: D

The correct answer is (1,−2)(1,-2).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: A 90-degree clockwise rotation uses (x,y)mapsto(y,−x)(x,y)\\mapsto(y,-x), so (2,1)mapsto(1,−2)(2,1)\\mapsto(1,-2).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

A 90-degree clockwise rotation uses (x,y)mapsto(y,−x)(x,y)\\mapsto(y,-x), so (2,1)mapsto(1,−2)(2,1)\\mapsto(1,-2).

5. QuestionMultiple choice

The point (−1,4)(-1,4) is translated 5 units left and 2 units up. What is its image?

Please select an answer first.

Correct answer: A

The correct answer is (−6,6)(-6,6).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Subtract 5 from x and add 2 to y: (−1−5,4+2)=(−6,6)(-1-5,4+2)=(-6,6).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Subtract 5 from x and add 2 to y: (−1−5,4+2)=(−6,6)(-1-5,4+2)=(-6,6).

6. QuestionMultiple choice

What is the reflection of (3,−2)(3,-2) across the line y=xy=x?

Please select an answer first.

Correct answer: B

The correct answer is (−2,3)(-2,3).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Reflection across y=xy=x switches the coordinates: (x,y)mapsto(y,x)(x,y)\\mapsto(y,x).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Reflection across y=xy=x switches the coordinates: (x,y)mapsto(y,x)(x,y)\\mapsto(y,x).

7. QuestionMultiple choice

What is the image of (4,−1)(4,-1) after a 180-degree rotation about the origin?

Please select an answer first.

Correct answer: C

The correct answer is (−4,1)(-4,1).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: A 180-degree rotation changes both signs: (x,y)mapsto(−x,−y)(x,y)\\mapsto(-x,-y).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

A 180-degree rotation changes both signs: (x,y)mapsto(−x,−y)(x,y)\\mapsto(-x,-y).

8. QuestionMultiple choice

Which rule represents a reflection across the x-axis?

Please select an answer first.

Correct answer: D

The correct answer is (x,y)mapsto(x,−y)(x,y)\\mapsto(x,-y).

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

The x-coordinate stays the same and the y-coordinate changes sign.

9. QuestionMultiple choice

The point (0,2)(0,2) is translated 4 units right. What is its image?

Please select an answer first.

Correct answer: A

The correct answer is (4,2)(4,2).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Add 4 to the x-coordinate and keep y unchanged: (0+4,2)=(4,2)(0+4,2)=(4,2).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Add 4 to the x-coordinate and keep y unchanged: (0+4,2)=(4,2)(0+4,2)=(4,2).

10. QuestionMultiple choice

Which property is preserved by every rigid transformation?

Please select an answer first.

Correct answer: B

The correct answer is Distances and angle measures.

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Translations, reflections, and rotations preserve lengths and angles, although orientation may reverse under reflection.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Translations, reflections, and rotations preserve lengths and angles, although orientation may reverse under reflection.

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