Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 6th grade coordinate plane? Then this Grade 6 lesson on Plotting Points and Shapes on the Coordinate Plane explains each idea step by step, with worked examples.
Quick answer: The coordinate plane is made by a horizontal x-axis and a vertical y-axis that meet at the origin (0, 0). An ordered pair (x, y) names a point: move x units left or right, then y units up or down. The signs of x and y show the quadrant, and reflecting across an axis flips one sign.
Standards: 6.NS.C.6b, 6.NS.C.6c, 6.NS.C.8, 6.G.A.3 · Level: Grade 6
How do ordered pairs locate points on the coordinate plane?
Two perpendicular number lines, the horizontal x-axis and the vertical y-axis, cross at the origin (0, 0). An ordered pair (x, y) gives a point: first move x units right (positive) or left (negative), then y units up (positive) or down (negative).
The axes split the plane into four quadrants. The signs of the coordinates tell you where a point lies.
| Quadrant | x | y | Example |
|---|---|---|---|
| I | + | + | (6, 2) |
| II | − | + | (−5, 4) |
| III | − | − | (−1, −7) |
| IV | + | − | (3, −6) |
A point with a 0 coordinate lies on an axis, not in a quadrant. Decimals and fractions work the same way: (−1.5, 2.5) is in Quadrant II.
How do reflections change a point?
- Across the x-axis: (x, y) becomes (x, −y).
- Across the y-axis: (x, y) becomes (−x, y).
How do you find the distance between two points?
- Check which coordinate matches. The other coordinate changes.
- Compare the changing coordinates. If they have different signs, add their absolute values; if the same sign, subtract the smaller absolute value from the larger.
- Label the answer in units.
Find the distance from (−4, 2) to (3, 2). The y-coordinates match, so the x-values differ: |−4| + |3| = 4 + 3 = 7 units.
How can you draw a polygon from its vertices?
Plot each vertex, then join them in order. Side lengths along a horizontal or vertical side come from the distance rule: in the rectangle below, the bottom side runs from x = −3 to x = 2, so it is 3 + 2 = 5 units, and the right side runs from y = −1 to y = 3, so it is 1 + 3 = 4 units.
Swapping the coordinates. The point (2, 5) is not (5, 2): the x-value always comes first.
Walk first, then climb: move along the floor for x, then up or down the stairs for y.
- Ordered pair (x, y): horizontal move first, vertical move second.
- Quadrants I, II, III, IV have signs (+,+), (−,+), (−,−), (+,−).
- Reflection across the x-axis changes y to −y; across the y-axis changes x to −x.
- Points sharing a coordinate are a horizontal or vertical distance apart.
- Points with a 0 coordinate lie on an axis and belong to no quadrant.
Plotting Points and Shapes on the Coordinate Plane: frequently asked questions
What does the order in (x, y) mean?
The first number is the horizontal position and the second is the vertical position. Reversing them gives a different point unless x and y are equal.
Which quadrant has two negative coordinates?
Quadrant III, the lower left. Both the x-value and the y-value are negative there, as in (−4, −9).
How do you reflect a point across the y-axis?
Keep the y-coordinate and change the sign of the x-coordinate. The point (5, −3) reflects to (−5, −3), the same distance from the y-axis on the other side.
How do you find the distance when the points have the same x-coordinate?
Use the y-coordinates. If their signs differ, add the absolute values; if they match, subtract. From (2, −6) to (2, 4), the distance is 6 + 4 = 10.
Is the point (0, 5) in a quadrant?
No. A point with a zero coordinate sits on an axis. (0, 5) is on the y-axis, 5 units above the origin.
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