Worked example 1
In which quadrant is (-3, 5)?
Start by writing the calculation clearly: x = -3 is negative (left of origin); y = 5 is positive (above origin). Negative x and positive y is Quadrant II.
Answer: Quadrant II
Grade 6 Math · Topic 29
The Coordinate Plane
The coordinate plane is formed by two perpendicular number lines: the horizontal x-axis and the vertical y-axis. They meet at the origin (0,0). Every point has an ordered pair (x,y): x tells you left/right, y tells you up/down. The plane is split into four quadrants.
Lesson alignment: 6.NS.C.6.c · 6.NS.C.8 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Measure a horizontal or vertical grid segment
Move the points along one shared coordinate. Count unit intervals and compare with the absolute difference.
Think first: Predict what will change when you adjust one value, then use the model to check your idea.
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Grade 6 core skill · 6.NS.C.8
Find distance between points on one grid line
When two points share the same y-coordinate, the segment is horizontal. Subtract their x-coordinates and take the absolute value. When they share the same x-coordinate, do the same with their y-coordinates.
Example: A(−3, 2) and B(4, 2)
The y-coordinates match, so move horizontally. Count from −3 to 0 (3 units), then 0 to 4 (4 more units).
Distance = |4 − (−3)| = 7 units
Distance is never negative. The absolute value gives the length of the segment.
Do not add the coordinates just because one is negative. Compare positions on the axis and count the unit intervals between them.
Quick check: C(5, −4) and D(5, 3)
The x-coordinates match, so the segment is vertical. |3 − (−4)| = 7 units.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Plot A(2,-4). Describe how you move from the origin.
From (0,0), move right 2 along the x-axis, then down 4 along the y-direction. A lands in Quadrant IV.
Answer: 2 right, 4 down (Quadrant IV).
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- (4, 7) →
Check
Quadrant I
- (-2, 6) →
Check
Quadrant II
- (-5, -3) →
Check
Quadrant III
- (8, -1) →
Check
Quadrant IV
- (0, 4) →
Check
y-axis
- (-6, 0) →
Check
x-axis
- (0, 0) →
Check
origin
- (3, -9) →
Check
Quadrant IV
Try this situation 1
A map uses a coordinate plane. The library is at (-4, 3) and the school is at (5, -2). Which quadrant is each in?
Show a worked solution
Answer: Library: Quadrant II. School: Quadrant IV.
Library has x<0, y>0 → II. School has x>0, y<0 → IV.
Try this situation 2
Where is the point (0, -7) located — on an axis or in a quadrant?
Show a worked solution
Answer: On the y-axis (below the origin).
Whenever x=0, the point is on the y-axis. y=-7 means 7 units below the origin.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.
More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.