Lesson 13: The Coordinate Plane and Graphing Points
The coordinate plane is a flat surface formed by two number lines:
- The horizontal number line is called the x-axis.
- The vertical number line is called the y-axis.
They intersect at the origin, \((0, 0)\). Points on the plane are located using ordered pairs \((x, y)\), where x is the horizontal value and y is the vertical value.
The Four Quadrants
The axes divide the plane into four regions called quadrants:
- Quadrant I: \(x > 0, y > 0\)
- Quadrant II: \(x < 0, y > 0\)
- Quadrant III: \(x < 0, y < 0\)
- Quadrant IV: \(x > 0, y < 0\)
Examples: Plotting Points
Let’s plot a few points on the coordinate plane:
- \((3, 2)\) → right 3, up 2 (Quadrant I)
- \((-2, 4)\) → left 2, up 4 (Quadrant II)
- \((-3, -1)\) → left 3, down 1 (Quadrant III)
- \((4, -2)\) → right 4, down 2 (Quadrant IV)
Practice Problems
Plot the following points on a coordinate plane and identify their quadrants:
- \((2, 5)\)
- \((-4, -3)\)
- \((0, 6)\)
- \((-5, 0)\)
Lesson Summary
- The coordinate plane has an x-axis (horizontal) and y-axis (vertical) that meet at the origin \((0,0)\).
- Points are located with ordered pairs \((x,y)\).
- The plane is divided into four quadrants based on the signs of \(x\) and \(y\).