Coordinate Geometry

Explore all four quadrants, reflections, and transformations!

6th Grade

🎮 Four Quadrant Grid

Point A: (2, 3) | Point B: (6, 7)

1. Four Quadrants

Coordinate plane: Two perpendicular number lines (x-axis horizontal, y-axis vertical) meeting at the origin $(0, 0)$ . Also called the Cartesian plane.

Quadrant I: $(+, +)$ - top right. Both coordinates positive. Examples: $(3, 4), (5, 2), (1, 7)$ .

Quadrant II: $(-, +)$ - top left. x negative, y positive. Examples: $(-3, 4), (-5, 2)$ .

Quadrant III: $(-, -)$ - bottom left. Both coordinates negative. Examples: $(-3, -4), (-5, -2)$ .

Quadrant IV: $(+, -)$ - bottom right. x positive, y negative. Examples: $(3, -4), (5, -2)$ .

Axes: Points on x-axis have $y = 0$ (e.g., $(5, 0), (-3, 0)$ ). Points on y-axis have $x = 0$ (e.g., $(0, 4), (0, -2)$ ). Origin is $(0, 0)$ .

Memory trick: "All Students Take Calculus" - starting from Quadrant I and going counterclockwise: All (I), Students (II), Take (III), Calculus (IV). Or remember: Quadrant I is like the first quadrant of a clock (top right).

2. Plotting Points

3. Distance Between Points

4. Translations

5. Reflections

6. Real-World Applications

Practice Time!

Practice Quiz

Questions

Correct

Score

In which quadrant is (-3, 4)?

In which quadrant is (5, -2)?

Reflect (3, 2) over x-axis?

Reflect (-4, 5) over y-axis?

Distance from (0,0) to (3, 4)?

Where is (-5, -3)?

Translate (2, 3) by (4, -1)?

Point on y-axis has x =?

Horizontal distance from (-2, 5) to (4, 5)?

Origin is at: