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Graph Points in
Four Quadrants

Learn to plot ordered pairs across every region of the coordinate plane, and use absolute value to find distances between points.

6th Grade Math

What Is the Coordinate Plane?

The coordinate plane is formed by two number lines that cross at a right angle. The horizontal line is the \(x\)-axis and the vertical line is the \(y\)-axis. Where they meet is the origin, located at \((0, 0)\).

x y -2 -1 1 2 3 1 2 -1 -2 (0, 0) Origin

Ordered Pairs: \((x, y)\)

Every point on the coordinate plane is described by an ordered pair \((x, y)\). The first number tells you how far to move left or right from the origin. The second number tells you how far to move up or down.

\(x\)-coordinate
Positive: move right. Negative: move left. Always move horizontally first.
\(y\)-coordinate
Positive: move up. Negative: move down. Always move vertically second.

The Four Quadrants

I (+, +) II (-, +) III (-, -) IV (+, -) x y (0, 0)

Sign Rules for Each Quadrant

Quadrant \(x\) sign \(y\) sign Example
I + + \((3, 5)\)
II - + \((-4, 2)\)
III - - \((-1, -6)\)
IV + - \((7, -3)\)

How to Plot a Point

1
Start at the origin \((0, 0)\).
2
Read the \(x\)-coordinate. Move right if positive, left if negative.
3
Read the \(y\)-coordinate. Move up if positive, down if negative.
4
Mark the point and label it with its ordered pair.

Example: Plot \((3, 3)\)

-2 -1 1 2 3 2 3 1 -1 -2 right 3 up 3 (3, 3)

Example: Plot \((-4, -2)\)

-1 -2 -3 -4 1 2 3 1 2 -1 -2 left 4 down 2 (-4, -2)

Example: Multiple Points

-3 -2 -1 1 2 3 1 2 3 -1 -2 A(2, 3) B(-3, 1) C(-2, -2) D(3, -1)
A(2, 3)
Quadrant I: both positive
B(-3, 1)
Quadrant II: \(x\) neg, \(y\) pos
C(-2, -2)
Quadrant III: both negative
D(3, -1)
Quadrant IV: \(x\) pos, \(y\) neg

Reflections Across the Axes

When you reflect a point across an axis, one coordinate changes sign while the other stays the same:

Reflect across \(x\)-axis
\((a, b) \to (a, -b)\). The \(y\)-coordinate flips sign.
Reflect across \(y\)-axis
\((a, b) \to (-a, b)\). The \(x\)-coordinate flips sign.

Distance Using Absolute Value

When two points share the same \(x\)-coordinate or the same \(y\)-coordinate, the distance between them is found using absolute value:

Same \(x\)-coordinate
Distance \(= |y_1 - y_2|\). The points are on a vertical line.
Same \(y\)-coordinate
Distance \(= |x_1 - x_2|\). The points are on a horizontal line.

Example: Finding Distance

1 2 3 -1 -2 1 2 3 -1 -2 P(2, 3) Q(2, -1) 4 units

Example: Horizontal Distance

-3 -2 -1 1 2 3 4 1 2 -1 -2 A(-3, -1) B(4, -1) 7 units

Reading vs Plotting Points

Task Reading a Point Plotting a Point
Given A dot on the grid An ordered pair
Step 1 Find horizontal position Move along \(x\)-axis
Step 2 Find vertical position Move along \(y\) direction
Result Write \((x, y)\) Draw the dot
Key skill Read the grid carefully Move in the correct order

Common Mistakes to Avoid

✕ Swapping \(x\) and \(y\)
Plotting \((3, 5)\) as up 3, right 5 instead of right 3, up 5. Always go horizontal first.
✕ Ignoring Negative Signs
Treating \((-2, 4)\) the same as \((2, 4)\). A negative \(x\) means move left, not right.
✕ Forgetting Absolute Value
Getting a negative distance like \(3 - 5 = -2\). Distance is always positive: \(|3 - 5| = 2\).

Quick Reference Summary

Concept Rule
Ordered pair \((x, y)\): horizontal, then vertical
Quadrant I \((+, +)\): upper right
Quadrant II \((-, +)\): upper left
Quadrant III \((-, -)\): lower left
Quadrant IV \((+, -)\): lower right
Vertical distance \(|y_1 - y_2|\) when \(x\) values match
Horizontal distance \(|x_1 - x_2|\) when \(y\) values match

Question 1 of 5

In which quadrant is the point \((-5, 3)\) located?

Question 2 of 5

What is the distance between \((4, -2)\) and \((4, 5)\)?

Question 3 of 5

Which ordered pair is located on the \(y\)-axis?

Question 4 of 5

If you reflect the point \((3, -4)\) across the \(x\)-axis, what are the new coordinates?

Question 5 of 5

What is the distance between \((-6, 2)\) and \((3, 2)\)?