∑∫ax²+bx+c=0π√x

On this page

By MathPal Editorial Team·PublishedApr 13, 2026·Updated Apr 14, 2026

Grade: 6–7 | Topic: Geometry

What You Will Learn

By the end of this page, you will be able to identify the x-axis, y-axis, origin, and four quadrants of the coordinate plane, plot any ordered pair (x,y) accurately, and read the coordinates of a point from a graph. This skill is the foundation for graphing equations and understanding geometry.

Theory

The Coordinate Plane

The coordinate plane (also called the Cartesian plane) is a flat grid formed by two perpendicular number lines:

• x-axis: horizontal number line (left = negative, right = positive)
• y-axis: vertical number line (down = negative, up = positive)
• Origin: the point where the axes cross, written as (0,0)

Ordered Pairs

Every point on the coordinate plane is described by an ordered pair (x,y):

• The x-coordinate (first number) tells you horizontal position
• The y-coordinate (second number) tells you vertical position

Always move horizontally (x) first, then vertically (y).

The Four Quadrants

Points on the axes belong to no quadrant: (5,0) is on the x-axis, (0,−2) is on the y-axis.

Worked Examples

Example 1: Plotting Points in All Four Quadrants

Problem: Plot the points A(4,3), B(−2,5), C(−3,−4), D(5,−1).

Point A(4, 3) — Quadrant I:

• Start at origin. Move 4 right, then 3 up. Mark the point.

Point B(-2, 5) — Quadrant II:

• Move 2 left, then 5 up. Mark the point.

Point C(-3, -4) — Quadrant III:

• Move 3 left, then 4 down. Mark the point.

Point D(5, -1) — Quadrant IV:

• Move 5 right, then 1 down. Mark the point.

Example 2: Reading Coordinates from a Graph

Problem: A point is located 3 units to the left of the y-axis and 7 units above the x-axis. What are its coordinates?

Step 1: Left of y-axis means negative x: x=−3.

Step 2: Above x-axis means positive y: y=7.

Answer: The point is (−3,7) — Quadrant II.

Example 3: Finding Distance Along a Horizontal or Vertical Line

Problem: Points P(2,4) and Q(8,4) are plotted. What is the distance between them?

Step 1: Both points have the same y-coordinate (4), so they lie on a horizontal line.

Step 2: Distance = difference in x-coordinates. ∣8−2∣=6

Answer: The distance is 6 units.

Example 4: Plotting a Shape

Problem: Plot the rectangle with vertices A(1,1), B(5,1), C(5,4), D(1,4). Find its area.

Step 1: Plot all four points and connect them in order.

Step 2: Width = horizontal distance from A to B = 5−1=4 units.

Step 3: Height = vertical distance from A to D = 4−1=3 units.

Step 4: Area = width × height. A=4×3=12 square units.

Answer: Area = 12 square units.

Common Mistakes

Mistake 1: Reversing x and y When Plotting

❌ To plot (3,7), student moves 7 right and 3 up.

✅ The first coordinate is always x (horizontal), second is y (vertical). (3,7): move 3 right, then 7 up.

Mistake 2: Moving in the Wrong Direction for Negative Coordinates

❌ For (−4,2), student moves 4 right (ignoring the negative sign).

✅ Negative x means left. Move 4 left, then 2 up.

Mistake 3: Confusing the Origin's Coordinates

❌ The origin is at (1,1).

✅ The origin is at (0,0) — the exact crossing point of the two axes.

Practice Problems

Try these on your own before checking the answers:

1. In which quadrant is the point (−5,3)?
2. Plot and describe the location of (0,−4).
3. What are the coordinates of a point 6 units right and 2 units below the origin?
4. Points M(−3,2) and N(−3,−5) lie on the same vertical line. What is the distance between them?
5. A square has one corner at (2,1) and the opposite corner at (6,5). What is its area?

Click to see answers

1. Quadrant II (negative x, positive y)
2. (0,−4) is on the y-axis, 4 units below the origin — not in any quadrant
3. (6,−2) — Quadrant IV
4. Same x-coordinate, so distance =∣2−(−5)∣=7 units
5. Side length =∣6−2∣=4 units. Area = 16 square units

Summary

• The coordinate plane has two axes: x (horizontal) and y (vertical), crossing at the origin (0,0).
• An ordered pair (x,y): always move horizontally first (x), then vertically (y).
• Negative x = left; positive x = right; negative y = down; positive y = up.
• The four quadrants are numbered I–IV counterclockwise from the top-right.