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Coordinate Geometry Practice Tests

These Grade 10 Geometry practice tests connect algebra and geometry through ordered pairs, transformations, distance, midpoint, slope, line equations, coordinate proofs, and real-world models.

Skills covered

  • Reading the coordinate plane, quadrants, ordered pairs, reflections, and translations
  • Using distance, midpoint, and slope formulas with exact values and units
  • Writing and interpreting slope-intercept, point-slope, and standard-form equations
  • Identifying parallel and perpendicular lines and proving points are collinear
  • Applying coordinate geometry to maps, ramps, fares, routes, gardens, dilations, and other practical situations

How to use these practice tests

Plot the points when useful, calculate changes in x and y, and keep track of negative signs. Use the distance formula for diagonal segments and slope comparisons for line relationships.

For more Grade 10 Math practice, return to the Grade 10 Math category.

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Grade 10 Coordinate Geometry Practice Tests

Practice Grade 10 Geometry questions about the coordinate plane, transformations, distance, midpoint, slope, linear equations, parallel and perpendicular lines, coordinate proofs, and applications.

Choose the best answer. Plot or read the points carefully, select the appropriate coordinate formula, and check signs, units, and slope relationships.

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

What is the slope of a line modeling a rate of change?

Please select an answer first.

Correct answer: A

The correct answer is The change in output divided by the change in input..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: Slope measures change in y per unit change in x.
  3. Check the result: The correct answer is The change in output divided by the change in input..

Slope measures change in y per unit change in x.

2. QuestionMultiple choice

A map uses points (1, 2) and (5, 5) for two locations. What is the slope between them?

Please select an answer first.

Correct answer: B

The correct answer is 34\frac{3}{4}..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: The slope is (5−2)/(5−1)=3/4(5-2)/(5-1)=3/4.
  3. Check the result: The correct answer is 34\frac{3}{4}..

The slope is (5−2)/(5−1)=3/4(5-2)/(5-1)=3/4.

3. QuestionMultiple choice

A wheelchair ramp rises 2 feet over a horizontal run of 24 feet. What is its slope?

Please select an answer first.

Correct answer: C

The correct answer is 112\frac{1}{12}..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: Slope is rise over run: 2/24=1/122/24=1/12.
  3. Check the result: The correct answer is 112\frac{1}{12}..

Slope is rise over run: 2/24=1/122/24=1/12.

4. QuestionMultiple choice

A taxi fare is modeled by y = 2.50x + 4. What does 4 represent?

Please select an answer first.

Correct answer: D

The correct answer is The starting fee..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: The y-intercept is the fare when x = 0, so it is the starting fee.
  3. Check the result: The correct answer is The starting fee..

The y-intercept is the fare when x = 0, so it is the starting fee.

5. QuestionMultiple choice

Where do the lines y = x + 2 and y = −x + 6 intersect?

Please select an answer first.

Correct answer: A

The correct answer is (2, 4)..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: Set the equations equal: x+2=−x+6, so x=2 and y=4.
  3. Check the result: The correct answer is (2, 4)..

Set the equations equal: x+2=−x+6, so x=2 and y=4.

6. QuestionMultiple choice

What is the midpoint of a 10-mile route from (2, 4) to (8, 10)?

Please select an answer first.

Correct answer: B

The correct answer is (5, 7)..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: The midpoint is ((2+8)/2,(4+10)/2)=(5,7)((2+8)/2,(4+10)/2)=(5,7).
  3. Check the result: The correct answer is (5, 7)..

The midpoint is ((2+8)/2,(4+10)/2)=(5,7)((2+8)/2,(4+10)/2)=(5,7).

7. QuestionMultiple choice

A rectangular garden has vertices (1, 1), (7, 1), (7, 5), and (1, 5). What is its area?

Please select an answer first.

Correct answer: C

The correct answer is 24 square units..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: The side lengths are 6 and 4, so the area is 6⋅4=246\cdot4=24.
  3. Check the result: The correct answer is 24 square units..

The side lengths are 6 and 4, so the area is 6⋅4=246\cdot4=24.

8. QuestionMultiple choice

Which point is on the line y = 2x − 3?

Please select an answer first.

Correct answer: D

The correct answer is (4, 5)..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: Substitute x=4: y=2(4)−3=5.
  3. Check the result: The correct answer is (4, 5)..

Substitute x=4: y=2(4)−3=5.

9. QuestionMultiple choice

A line passes through (3, 2) with slope −2. What is y when x = 5?

Please select an answer first.

Correct answer: A

The correct answer is −2..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: Use point-slope reasoning: y−2=−2(5−3), giving y=−2.
  3. Check the result: The correct answer is −2..

Use point-slope reasoning: y−2=−2(5−3), giving y=−2.

10. QuestionMultiple choice

A design is enlarged by a scale factor of 3. How does each coordinate change from the origin?

Please select an answer first.

Correct answer: B

The correct answer is Each coordinate is multiplied by 3..

  1. Identify the coordinate information: Read the ordered pairs, slope, equation, or geometric relationship given in the problem.
  2. Apply the coordinate formula or rule: A dilation centered at the origin sends (x,y) to (3x,3y).
  3. Check the result: The correct answer is Each coordinate is multiplied by 3..

A dilation centered at the origin sends (x,y) to (3x,3y).

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