NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

2. 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

Apply (x,y)mapsto(x+2,y+1)(x,y)\\mapsto(x+2,y+1) to the point (3,4)(3,4).

Please select an answer first.

Correct answer: A

The correct answer is (5,5)(5,5).

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

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

2. QuestionMultiple choice

Apply a reflection across the x-axis to (−2,5)(-2,5).

Please select an answer first.

Correct answer: B

The correct answer is (−2,−5)(-2,-5).

  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 -2 and the y-coordinate changes from 5 to -5.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

The x-coordinate stays -2 and the y-coordinate changes from 5 to -5.

3. QuestionMultiple choice

Apply a reflection across the y-axis to (6,−1)(6,-1).

Please select an answer first.

Correct answer: C

The correct answer is (−6,−1)(-6,-1).

  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-coordinate stays -1 and the x-coordinate changes from 6 to -6.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

The y-coordinate stays -1 and the x-coordinate changes from 6 to -6.

4. QuestionMultiple choice

What is the image of (−3,2)(-3,2) after a 180-degree rotation about the origin?

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: Change both coordinate signs: (−3,2)mapsto(3,−2)(-3,2)\\mapsto(3,-2).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Change both coordinate signs: (−3,2)mapsto(3,−2)(-3,2)\\mapsto(3,-2).

5. QuestionMultiple choice

What is the reflection of (7,1)(7,1) across y=xy=x?

Please select an answer first.

Correct answer: A

The correct answer is (1,7)(1,7).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Switch the coordinates to get (1,7)(1,7).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Switch the coordinates to get (1,7)(1,7).

6. QuestionMultiple choice

A point (2,3)(2,3) is rotated 90 degrees counterclockwise about the origin. What is its image?

Please select an answer first.

Correct answer: B

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: A 90-degree counterclockwise rotation uses (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.

A 90-degree counterclockwise rotation uses (x,y)mapsto(−y,x)(x,y)\\mapsto(-y,x).

7. QuestionMultiple choice

Apply the translation (x,y)mapsto(x−4,y+6)(x,y)\\mapsto(x-4,y+6) to (5,−2)(5,-2).

Please select an answer first.

Correct answer: C

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

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

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

8. QuestionMultiple choice

What is the reflection of (2,−5)(2,-5) across the line y=−xy=-x?

Please select an answer first.

Correct answer: D

The correct answer is (5,−2)(5,-2).

  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 uses (x,y)mapsto(−y,−x)(x,y)\\mapsto(-y,-x), giving (5,−2)(5,-2).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Reflection across y=−xy=-x uses (x,y)mapsto(−y,−x)(x,y)\\mapsto(-y,-x), giving (5,−2)(5,-2).

9. QuestionMultiple choice

What is the image of (2,−1)(2,-1) after a dilation centered at the origin with scale factor 3?

Please select an answer first.

Correct answer: A

The correct answer is (6,−3)(6,-3).

  1. Identify the transformation: Read whether the figure is translated, reflected, rotated, or resized and identify its coordinate rule.
  2. Apply the rule: Multiply both coordinates by 3: (3cdot2,3cdot(−1))=(6,−3)(3\\cdot2,3\\cdot(-1))=(6,-3).
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

Multiply both coordinates by 3: (3cdot2,3cdot(−1))=(6,−3)(3\\cdot2,3\\cdot(-1))=(6,-3).

10. QuestionMultiple choice

Which rule represents the identity transformation?

Please select an answer first.

Correct answer: B

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 identity transformation leaves every point unchanged.
  3. Check congruence: Compare corresponding side lengths and angle measures to determine whether the transformation preserves size and shape.

The identity transformation leaves every point unchanged.

Previous testNext test