The Coordinate Plane

Grade 6 Mathematics

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The Big Idea

The coordinate plane extends in ALL DIRECTIONS from the origin (0, 0)!

An ordered pair (x, y) tells you exactly where a point is located. The x-coordinate tells you how far LEFT or RIGHT, and the y-coordinate tells you how far UP or DOWN.

Positive x = RIGHT, Negative x = LEFT | Positive y = UP, Negative y = DOWN

The Four Quadrants

The coordinate plane is divided into 4 sections called quadrants, numbered with Roman numerals going counter-clockwise from the upper right:

Quadrant II
( - , + )
x is negative
y is positive
Quadrant I
( + , + )
x is positive
y is positive
Quadrant III
( - , - )
x is negative
y is negative
Quadrant IV
( + , - )
x is positive
y is negative

Memory trick: Start at Quadrant I (top right) and go counter-clockwise!

Example 1: Plotting Points with Negative Coordinates

Plot the point (-4, 3)

1

Start at the origin (0, 0) - where the x-axis and y-axis cross.

2

Look at the x-coordinate: -4. The negative sign means move LEFT 4 units.

3

Look at the y-coordinate: 3. The positive sign means move UP 3 units.

4

Mark your point! This point is in Quadrant II (x is negative, y is positive).

Example 2: Finding Distance Between Points

Find the distance from point A (3, -2) to point B (3, 5)

Notice: Both points have the SAME x-coordinate (3).

When points share an x-coordinate, they're on the same vertical line!

1

Same x-coordinate? YES! So we use the y-coordinates to find distance.

2

Subtract the y-coordinates: |5 - (-2)| = |5 + 2| = |7| = 7 units

Remember: Use absolute value because distance is always positive!

TRAP ALERT: Don't Mix Up X and Y!

WRONG: For point (5, -3), going UP 5 and RIGHT 3.

RIGHT: X comes FIRST - go RIGHT 5, then y-coordinate DOWN 3. Remember: "X marks the spot horizontally first!"

Your Turn: Identify the Quadrant

1. Point (-6, -4) is in Quadrant

x is _________ (positive/negative), y is _________ (positive/negative)

2. Point (7, -2) is in Quadrant

x is _________ (positive/negative), y is _________ (positive/negative)

3. Point (-3, 8) is in Quadrant

4. Point (0, -5) is on the axis.

(Hint: When x = 0, the point is on which axis?)

Your Turn: Find the Distance

5. Distance from (4, 2) to (4, -6) = units

Same x-coordinate? _____ Use y-coordinates: |2 - (-6)| = _____

6. Distance from (-3, 5) to (7, 5) = units

Same y-coordinate? _____ Use x-coordinates: |7 - (-3)| = _____

Remember These Key Points!