The coordinate plane (grade 5) · lesson

x first, y second

💡 In a point (x, y), the first number is how far right and the second is how far up.

Every point has two numbers. The first is the x-coordinate. The second is the y-coordinate.

In (4, 3), x is 4 and y is 3.

🧠 Let's work it out

What is the y-coordinate of (8, 1)?

What do you think comes next?

💡 From (0, 0), go right for x first, then go up for y.

The point (0, 0) is where the two lines meet. It is called the origin.

Move right first. That is x. Then move up. That is y.

🧠 Let's work it out

Start at (0, 0). Move 2 right and 7 up. Where do you land?

What do you think comes next?

💡 Moving right or left changes only x, and moving up or down changes only y.

Right adds to x. Left takes away from x. The y stays the same.

Up adds to y. Down takes away from y. The x stays the same.

🧠 Let's work it out

Move (3, 6) 2 units left.

What do you think comes next?

💡 Points on the x-axis have y = 0, and points on the y-axis have x = 0.

The x-axis is the line going across. The y-axis is the line going up.

A point on the x-axis has not moved up at all, so its y is 0. (5, 0) is on the x-axis. (0, 4) is on the y-axis.

🧠 Let's work it out

Is (0, 9) on the x-axis or the y-axis?

What do you think comes next?

💡 When two points share an x or a y, subtract the other numbers to find how far apart they are.

(3, 2) and (3, 8) have the same x. One is straight above the other. 8 − 2 = 6, so they are 6 units apart.

You can use this to find the sides of a rectangle from its corners. Then add the sides to get the perimeter.

🧠 Let's work it out

A rectangle has corners (2, 1), (7, 1), (7, 3), (2, 3). What is its perimeter?

What do you think comes next?