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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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2. Test

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 distance between (1, 2) and (4, 6)?

Please select an answer first.

Correct answer: A

The correct answer is 5 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: Use the distance formula: d=(4−1)2+(6−2)2=25=5d=\sqrt{(4-1)^2+(6-2)^2}=\sqrt{25}=5.
  3. Check the result: The correct answer is 5 units..

Use the distance formula: d=(4−1)2+(6−2)2=25=5d=\sqrt{(4-1)^2+(6-2)^2}=\sqrt{25}=5.

2. QuestionMultiple choice

What is the midpoint of (−2, 5) and (6, 1)?

Please select an answer first.

Correct answer: B

The correct answer is (2, 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: Average the coordinates: M=((−2+6)/2,(5+1)/2)=(2,3)M=((−2+6)/2,(5+1)/2)=(2,3).
  3. Check the result: The correct answer is (2, 3)..

Average the coordinates: M=((−2+6)/2,(5+1)/2)=(2,3)M=((−2+6)/2,(5+1)/2)=(2,3).

3. QuestionMultiple choice

What is the slope of the line through (2, 3) and (6, 11)?

Please select an answer first.

Correct answer: C

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: The slope is m=(11−3)/(6−2)=8/4=2m=(11-3)/(6-2)=8/4=2.
  3. Check the result: The correct answer is 2..

The slope is m=(11−3)/(6−2)=8/4=2m=(11-3)/(6-2)=8/4=2.

4. QuestionMultiple choice

What is the slope of a horizontal line?

Please select an answer first.

Correct answer: D

The correct answer is 0..

  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 horizontal line has no vertical change, so m=0m=0.
  3. Check the result: The correct answer is 0..

A horizontal line has no vertical change, so m=0m=0.

5. QuestionMultiple choice

What is the slope of a vertical line?

Please select an answer first.

Correct answer: A

The correct answer is Undefined..

  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 vertical line has zero horizontal change, so division by zero makes its slope undefined.
  3. Check the result: The correct answer is Undefined..

A vertical line has zero horizontal change, so division by zero makes its slope undefined.

6. QuestionMultiple choice

A line rises 9 units while running 3 units. What is its slope?

Please select an answer first.

Correct answer: B

The correct answer is 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: Slope is rise over run: m=9/3=3m=9/3=3.
  3. Check the result: The correct answer is 3..

Slope is rise over run: m=9/3=3m=9/3=3.

7. QuestionMultiple choice

What is the distance between (−1, −2) and (2, 2)?

Please select an answer first.

Correct answer: C

The correct answer is 5 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: Use d=(2+1)2+(2+2)2=25=5d=\sqrt{(2+1)^2+(2+2)^2}=\sqrt{25}=5.
  3. Check the result: The correct answer is 5 units..

Use d=(2+1)2+(2+2)2=25=5d=\sqrt{(2+1)^2+(2+2)^2}=\sqrt{25}=5.

8. QuestionMultiple choice

What is the midpoint of (4, −6) and (10, 2)?

Please select an answer first.

Correct answer: D

The correct answer is (7, −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: Average each coordinate: M=((4+10)/2,(−6+2)/2)=(7,−2)M=((4+10)/2,(-6+2)/2)=(7,-2).
  3. Check the result: The correct answer is (7, −2)..

Average each coordinate: M=((4+10)/2,(−6+2)/2)=(7,−2)M=((4+10)/2,(-6+2)/2)=(7,-2).

9. QuestionMultiple choice

A segment has endpoints (−5, 4) and (3, 4). What is its length?

Please select an answer first.

Correct answer: A

The correct answer is 8 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 segment is horizontal, so its length is ∣3−(−5)∣=8|3-(-5)|=8.
  3. Check the result: The correct answer is 8 units..

The segment is horizontal, so its length is ∣3−(−5)∣=8|3-(-5)|=8.

10. QuestionMultiple choice

Which formula gives the slope between (x₁,y₁) and (x₂,y₂)?

Please select an answer first.

Correct answer: B

The correct answer is m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}..

  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 compares the change in y with the change in x.
  3. Check the result: The correct answer is m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}..

Slope compares the change in y with the change in x.

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