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Coordinate Plane Foundations

A free Pre-Algebra lesson from the “Coordinate Plane, Functions, and Slope” unit, with a worked example and practice problems including step-by-step solutions.

The coordinate plane uses two number lines. The x-axis runs left and right, and the y-axis runs up and down. An ordered pair is written (x, y), so the first number tells horizontal movement and the second number tells vertical movement.

What you'll learn

Why it matters: Maps, video-game positions, weather radar, and stadium seating charts all use coordinates. Two numbers locate any point uniquely.

Worked example

Problem. What quadrant contains the point (-3, 5)?

  1. The x-coordinate is negative, so move left.
  2. The y-coordinate is positive, so move up.
  3. Left and up is Quadrant II.

Answer: Quadrant II

Practice problems

1. In the point (4, -2), what is the x-coordinate?

Show solution
  1. Warm-up: First identify exactly what the question is asking: In the point (4, -2), what is the x-coordinate?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The x-coordinate is the first number.
  4. The first number is 4.
  5. Check the result by substituting or estimating: the response should match 4 and make sense in the original problem.

Answer: 4

2. In the point (-6, 3), what is the y-coordinate?

Show solution
  1. Warm-up: First identify exactly what the question is asking: In the point (-6, 3), what is the y-coordinate?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. The y-coordinate is the second number.
  4. The second number is 3.
  5. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.

Answer: 3

3. Which point is on the y-axis?

Choices: (0, 5) · (5, 0) · (3, 3) · (-2, 4)

Show solution
  1. Warm-up: First identify exactly what the question is asking: Which point is on the y-axis?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Points on the y-axis have x = 0.
  4. (0, 5) has x = 0.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: (0, 5)

4. Which quadrant contains (2, 7)?

Choices: Quadrant I · Quadrant II · Quadrant III · Quadrant IV

Show solution
  1. Core Practice: First identify exactly what the question is asking: Which quadrant contains (2, 7)?
  2. Compare each answer choice with the calculation or rule, and eliminate choices that do not satisfy the condition.
  3. Both coordinates are positive.
  4. Positive x and positive y is Quadrant I.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Quadrant I

5. Which quadrant contains (-5, -1)?

Choices: Quadrant I · Quadrant II · Quadrant III · Quadrant IV

Show solution
  1. Core Practice: First identify exactly what the question is asking: Which quadrant contains (-5, -1)?
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. Both coordinates are negative.
  4. Negative x and negative y is Quadrant III.
  5. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Quadrant III

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