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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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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

What is the image of (−2,5)(-2,5) under a dilation centered at the origin with scale factor 3?

Please select an answer first.

Correct answer: A

The correct answer is (−6,15)(-6,15).

  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 3: (−2,5)mapsto(−6,15)(-2,5)\\mapsto(-6,15).
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply both coordinates by 3: (−2,5)mapsto(−6,15)(-2,5)\\mapsto(-6,15).

2. QuestionMultiple choice

What is the image of (−8,4)(-8,4) under a dilation with scale factor frac12\\frac{1}{2}?

Please select an answer first.

Correct answer: B

The correct answer is (−4,2)(-4,2).

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

Multiply both coordinates by frac12\\frac{1}{2}.

3. QuestionMultiple choice

A triangle has area 12. What is its image area after a dilation with scale factor 2?

Please select an answer first.

Correct answer: C

The correct answer is 4848 square units.

  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 22=42^2=4, so 4(12)=484(12)=48.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Area scales by 22=42^2=4, so 4(12)=484(12)=48.

4. QuestionMultiple choice

A figure has perimeter 18. What is its image perimeter after a dilation with scale factor frac13\\frac{1}{3}?

Please select an answer first.

Correct answer: D

The correct answer is 66.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Perimeter scales linearly: frac13(18)=6\\frac{1}{3}(18)=6.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Perimeter scales linearly: frac13(18)=6\\frac{1}{3}(18)=6.

5. QuestionMultiple choice

What is the image of (1,−3)(1,-3) under a dilation centered at the origin with scale factor 4?

Please select an answer first.

Correct answer: A

The correct answer is (4,−12)(4,-12).

  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 4: (4,−12)(4,-12).
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply each coordinate by 4: (4,−12)(4,-12).

6. QuestionMultiple choice

A point has image (15,−6)(15,-6) after a dilation with scale factor 3. What was the original point?

Please select an answer first.

Correct answer: B

The correct answer is (5,−2)(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: Divide each image coordinate by 3: (15div3,−6div3)=(5,−2)(15\\div3,-6\\div3)=(5,-2).
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Divide each image coordinate by 3: (15div3,−6div3)=(5,−2)(15\\div3,-6\\div3)=(5,-2).

7. QuestionMultiple choice

An original side is 7 units and its image is 14 units. What is the scale factor?

Please select an answer first.

Correct answer: C

The correct answer is 22.

  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 14div7=214\\div7=2.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Calculate 14div7=214\\div7=2.

8. QuestionMultiple choice

What is the image of (12,8)(12,8) under a dilation centered at the origin with scale factor frac14\\frac{1}{4}?

Please select an answer first.

Correct answer: D

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

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Multiply each coordinate by frac14\\frac{1}{4}: (3,2)(3,2).
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply each coordinate by frac14\\frac{1}{4}: (3,2)(3,2).

9. QuestionMultiple choice

An image has area 75 after a dilation with scale factor 5. What was the original area?

Please select an answer first.

Correct answer: A

The correct answer is 33 square units.

  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 52=255^2=25, so the original area is 75div25=375\\div25=3.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Area scales by 52=255^2=25, so the original area is 75div25=375\\div25=3.

10. QuestionMultiple choice

A segment is dilated with scale factor 2. What happens to its distance from the center of dilation?

Please select an answer first.

Correct answer: B

The correct answer is It doubles..

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Every distance from the center is multiplied by the scale factor 2.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Every distance from the center is multiplied by the scale factor 2.

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