Explanation
The coordinate plane is a flat, two-dimensional surface used to locate points.
It is also called the Cartesian plane or the \(xy\)-plane.
The coordinate plane has two number lines:
- the \(x\)-axis, which is horizontal
- the \(y\)-axis, which is vertical
The two axes meet at the origin:
$$(0,0)$$
In \(1D\), we need only one value to locate a point on a number line.
In \(2D\), we need two values to locate a point. These values are written as an ordered pair:
$$(x,y)$$
The first value tells us the horizontal position, and the second value tells us the vertical position.
Formula / Rule
A point on the coordinate plane is written as:
$$(x,y)$$
Where:
- \(x\) gives the horizontal position.
- \(y\) gives the vertical position.
To plot a point:
- Start at the origin \((0,0)\).
- Use the \(x\)-coordinate to move right or left.
- Use the \(y\)-coordinate to move up or down.
- Mark the point.
Remember:
- \(x>0 \longrightarrow\) move right
- \(x<0 \longrightarrow\) move left
- \(y>0 \longrightarrow\) move up
- \(y<0 \longrightarrow\) move down
If \(x=0\), there is no horizontal movement, so the point lies on the \(y\)-axis.
If \(y=0\), there is no vertical movement, so the point lies on the \(x\)-axis.
Example
Plot the point:
$$P=(-2,3)$$
Step 1: Start at the origin.
$$(0,0)$$
Step 2: Look at the x-coordinate.
The \(x\)-coordinate is \(-2\).
Move \(2\) units to the left.
Step 3: Look at the \(y\)-coordinate.
The \(y\)-coordinate is \(3\).
Move \(3\) units up.
Step 4: Mark the point.
The point is:
$$P=(-2,3)$$
So, to plot \((-2,3)\), move \(2\) units left and \(3\) units up from the origin.
Video Explanation
Practice
Continue Learning
- Plotting Points on the Coordinate Plane (\(2D\)) (Current lesson)
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- Distance between Two Points in \(2D\)
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