Introduction to the Coordinate Plane
The coordinate plane is a fundamental concept in Algebra I, where we plot points and graph equations. It consists of two perpendicular lines: the x-axis and the y-axis, which intersect at the origin (0,0). This plane helps us to understand how variables interact with each other in a visual manner.
Outline
- Introduction to the Coordinate Plane
- The X-axis and Y-axis
- Plotting Points
- Examples
- Exercises with Solutions
- Homework
- Revision Section
- Contact Us for Tutoring
The Coordinate Plane
The coordinate plane is divided into four quadrants by the x-axis and y-axis. Each point on the plane is represented by an ordered pair \((x, y)\), where \(x\) is the horizontal position and \(y\) is the vertical position.
Figure: A coordinate plane with labeled axes and quadrants.
Examples of Plotting Points
Example 1:
Plot the point \((3, 4)\). To plot this point, move 3 units to the right on the x-axis and 4 units up on the y-axis.
Example 2:
Plot the point \((-2, -3)\). To plot this point, move 2 units to the left on the x-axis and 3 units down on the y-axis.
Example 3:
Plot the point \((0, 5)\). This point lies directly on the y-axis, 5 units above the origin.
Example 4:
Plot the point \((6, 0)\). This point lies directly on the x-axis, 6 units to the right of the origin.
Example 5:
Plot the point \((-4, 2)\). To plot this point, move 4 units to the left on the x-axis and 2 units up on the y-axis.
Example 6:
Plot the point \((3, -2)\). To plot this point, move 3 units to the right on the x-axis and 2 units down on the y-axis.
Exercises
Practice Problems:
- Plot the point \((4, -1)\)
- Plot the point \((-5, 3)\)
- Plot the point \((0, -6)\)
- Plot the point \((7, 2)\)
- Plot the point \((-3, -4)\)
- Plot the point \((2, 0)\)
Solutions:
1. Move 4 units right, 1 unit down.
2. Move 5 units left, 3 units up.
3. Move 6 units down.
4. Move 7 units right, 2 units up.
5. Move 3 units left, 4 units down.
6. Move 2 units right.
Homework
Homework Problems:
- Plot the following points: \((5, 6)\), \((-7, 4)\), \((0, -8)\), \((3, 5)\), \((-2, -3)\)
- Draw the coordinate plane and label all four quadrants.
Revision Section
Key points to remember:
- The coordinate plane consists of two perpendicular axes: x-axis and y-axis.
- Points are plotted based on their x and y coordinates.
- The origin is the point \((0,0)\) where the axes intersect.
Watch the Video Tutorial
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