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Similarity and Dilations Practice Tests

These Grade 8 Math practice tests cover similar figures, dilations, scale factors, coordinate rules, proportional sides, perimeters, areas, and real-world models.

Skills covered

  • Finding and applying scale factors
  • Using coordinate rules for dilations centered at the origin
  • Determining whether figures are similar or congruent
  • Scaling lengths, perimeters, and areas
  • Solving map, model, shadow, blueprint, and scale-drawing problems

How to use these practice tests

Match corresponding parts first. Use the image-to-original ratio as the scale factor, then apply \(k\) to lengths and \(k^2\) to areas.

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

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5 Tests
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1. Test

Grade 8 Similarity and Dilations Practice Tests

Practice Grade 8 Math questions about similar figures, dilations, scale factors, coordinate rules, proportional sides, perimeters, areas, and applications.

Choose the best answer for each question. Compare corresponding lengths, use the scale factor, and remember that areas scale by the square of the factor.

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

A dilation centered at the origin has scale factor 2. What is the image of (3,4)(3,4)?

Please select an answer first.

Correct answer: A

The correct answer is (6,8)(6,8).

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Multiply both coordinates by 2: (2cdot3,2cdot4)=(6,8)(2\\cdot3,2\\cdot4)=(6,8).
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply both coordinates by 2: (2cdot3,2cdot4)=(6,8)(2\\cdot3,2\\cdot4)=(6,8).

2. QuestionMultiple choice

A dilation centered at the origin has scale factor frac12\\frac{1}{2}. What is the image of (8,−6)(8,-6)?

Please select an answer first.

Correct answer: B

The correct answer is (4,−3)(4,-3).

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Multiply each coordinate by frac12\\frac{1}{2}: (4,−3)(4,-3).
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply each coordinate by frac12\\frac{1}{2}: (4,−3)(4,-3).

3. QuestionMultiple choice

A segment of length 5 is dilated by scale factor 3. What is the image length?

Please select an answer first.

Correct answer: C

The correct answer is 1515.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Multiply the original length by the scale factor: 3(5)=153(5)=15.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply the original length by the scale factor: 3(5)=153(5)=15.

4. QuestionMultiple choice

An image segment has length 12 after a dilation with scale factor 4. What was the original length?

Please select an answer first.

Correct answer: D

The correct answer is 33.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Divide the image length by the scale factor: 12div4=312\\div4=3.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Divide the image length by the scale factor: 12div4=312\\div4=3.

5. QuestionMultiple choice

A figure has perimeter 20. What is its perimeter after a dilation with scale factor 2?

Please select an answer first.

Correct answer: A

The correct answer is 4040.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Perimeters scale by k, so 2(20)=402(20)=40.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Perimeters scale by k, so 2(20)=402(20)=40.

6. QuestionMultiple choice

A square has area 4. What is its area after a dilation with scale factor 3?

Please select an answer first.

Correct answer: B

The correct answer is 3636.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Area scales by k2k^2: 32(4)=9(4)=363^2(4)=9(4)=36.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Area scales by k2k^2: 32(4)=9(4)=363^2(4)=9(4)=36.

7. QuestionMultiple choice

A side of length 4 is matched with an image side of length 10. What is the scale factor?

Please select an answer first.

Correct answer: C

The correct answer is frac52\\frac{5}{2}.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: The scale factor is image divided by original: 10div4=frac5210\\div4=\\frac{5}{2}.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

The scale factor is image divided by original: 10div4=frac5210\\div4=\\frac{5}{2}.

8. QuestionMultiple choice

Which rule represents a dilation centered at the origin with scale factor 3?

Please select an answer first.

Correct answer: D

The correct answer is (x,y)mapsto(3x,3y)(x,y)\\mapsto(3x,3y).

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: A centered dilation multiplies both coordinates by the scale factor.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

A centered dilation multiplies both coordinates by the scale factor.

9. QuestionMultiple choice

An original segment has length 6 and its image has length 18. What is the scale factor?

Please select an answer first.

Correct answer: A

The correct answer is 33.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Calculate 18div6=318\\div6=3.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Calculate 18div6=318\\div6=3.

10. QuestionMultiple choice

What does a dilation with scale factor 1 do to a figure?

Please select an answer first.

Correct answer: B

The correct answer is It leaves the size unchanged..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Multiplying every length by 1 produces the same figure size and shape.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiplying every length by 1 produces the same figure size and shape.

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