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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

A map uses 1 centimeter to represent 12 miles. How many miles does 3 centimeters represent?

Please select an answer first.

Correct answer: A

The correct answer is 3636 miles.

  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 map distance by the scale: 3(12)=363(12)=36 miles.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply the map distance by the scale: 3(12)=363(12)=36 miles.

2. QuestionMultiple choice

A model uses scale 1:501:50. An object measures 2 centimeters on the model. What is its actual length?

Please select an answer first.

Correct answer: B

The correct answer is 100100 centimeters.

  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 by 50: 2(50)=1002(50)=100 centimeters.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply by 50: 2(50)=1002(50)=100 centimeters.

3. QuestionMultiple choice

A 6-foot pole casts a 4-foot shadow. A tree casts a 10-foot shadow at the same time. How tall is the tree?

Please select an answer first.

Correct answer: C

The correct answer is 1515 feet.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Set the similar-triangle ratio: frac64=frach10\\frac{6}{4}=\\frac{h}{10}, so h=15h=15.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Set the similar-triangle ratio: frac64=frach10\\frac{6}{4}=\\frac{h}{10}, so h=15h=15.

4. QuestionMultiple choice

A drawing uses 1 inch to represent 2 feet. A room is 8 inches long in the drawing. How long is the room?

Please select an answer first.

Correct answer: D

The correct answer is 1616 feet.

  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 drawing length by 2: 8(2)=168(2)=16 feet.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply the drawing length by 2: 8(2)=168(2)=16 feet.

5. QuestionMultiple choice

A length of 8 is enlarged by scale factor 1.51.5. What is the image length?

Please select an answer first.

Correct answer: A

The correct answer is 1212.

  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 1.5(8)=121.5(8)=12.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Calculate 1.5(8)=121.5(8)=12.

6. QuestionMultiple choice

An original photo width is 16 centimeters and the enlarged image width is 24 centimeters. What is the scale factor?

Please select an answer first.

Correct answer: B

The correct answer is 1.51.5.

  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 image by original: 24div16=1.524\\div16=1.5.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Divide image by original: 24div16=1.524\\div16=1.5.

7. QuestionMultiple choice

A 5-foot pole casts an 8-foot shadow. A building casts a 20-foot shadow. How tall is the building?

Please select an answer first.

Correct answer: C

The correct answer is 12.512.5 feet.

  1. Identify the scale relationship: Compare a corresponding image length with its original length to find the scale factor.
  2. Apply the scale factor: Use frac58=frach20\\frac{5}{8}=\\frac{h}{20}, so h=12.5h=12.5 feet.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Use frac58=frach20\\frac{5}{8}=\\frac{h}{20}, so h=12.5h=12.5 feet.

8. QuestionMultiple choice

A map scale is 1 centimeter to 10 kilometers. A route measures 7 centimeters. What is the actual distance?

Please select an answer first.

Correct answer: D

The correct answer is 7070 kilometers.

  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 7(10)=707(10)=70 kilometers.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Multiply 7(10)=707(10)=70 kilometers.

9. QuestionMultiple choice

A blueprint shows 6 centimeters for an actual length of 24 meters. What actual length corresponds to 10 centimeters?

Please select an answer first.

Correct answer: A

The correct answer is 4040 meters.

  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 is 4 meters per centimeter, so 10(4)=4010(4)=40 meters.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

The scale is 4 meters per centimeter, so 10(4)=4010(4)=40 meters.

10. QuestionMultiple choice

An image side is 18 units after a dilation with scale factor 3. What was the original side?

Please select an answer first.

Correct answer: B

The correct answer is 66 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: Divide the image length by 3: 18div3=618\\div3=6.
  3. Check similarity and size: Lengths scale by k, perimeters by k, and areas by k squared.

Divide the image length by 3: 18div3=618\\div3=6.

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