Cartesian Plane/Coordinates (Junior Cert Mathematics): Revision Notes

The Co-ordinate Plane

What is the Cartesian Plane?

The Cartesian Plane is like a map that helps us find the location of points. It's made up of two lines:

• The $x-axis$: This is the horizontal line that goes left and right.
• The $y-axis$: This is the vertical line that goes up and down. These two lines meet at a special point called the origin. The origin is at ($0, 0$), where both the $x-axis$ and $y-axis$ cross each other.

How Do We Describe a Point?

To describe a point on this plane, we use two numbers called coordinates. These coordinates are written in brackets like this: $(x, y)$. Here's what they mean:

• $x:$ The first number tells us how far to move left or right from the origin.
• $y:$ The second number tells us how far to move up or down.

How to Plot Points on the Cartesian Plane

When you want to plot (or draw) a point on the Cartesian Plane, follow these simple steps:

1. Start at the Origin $(0, 0)$: Always begin at the origin, where the $x-axis$ and $y-axis$ cross.
2. Look at the $x-coordinate$: This is the first number. If it's positive, move to the right. If it's negative, move to the left. Don't move up or down yet, just go left or right.
3. Look at the $y-coordinate$: This is the second number. If it's positive, move up. If it's negative, move down. Start from where you stopped in step $2$, and now go up or down.
4. Mark the Point: After moving according to the $x$ and $y$ coordinates, place a dot to mark your point. Label it with the coordinates so you remember where it is.

Why is this Important?

Understanding how to plot points on the Cartesian Plane is a key skill in co-ordinate geometry. It will help you with more complex topics later on, like drawing lines or finding distances between points.