# Coordinates

## Writing Coordinates

We use coordinates to describe the position of a point on a grid.

Here we have a grid. On the grid is point A.

On the grid we have an x axis (which runs horizontally) and a y axis (which runs vertically).

We write coordinates in the form (x, y).
We always write the x coordinate before the y coordinate.

The x coordinate of A is 1. It is 1 along the x axis.
The y coordinate of A is 3. It is 3 up the y axis.

The coordinates of A are (1, 3).

Here we have another grid. On the grid is point B.

The x coordinate of B is -3. It is -3 along the x axis.
The y coordinate of B is -2 because it is 2 down the y axis.

The coordinates of B are (-3, -2).

Try these:

Write down the coordinates of point A.

Write down the coordinates of point B.

Write down the coordinates of point C.

## Finding the Midpoint of a Line Segment

On the grid we have a line AB (the line runs from A to B).

We can find the midpoint of the line by counting how far along the x axis and how far down the y axis we need to go to get from A to B.

We need to go 6 along the x axis to get from A to B.
We need to go 4 down the y axis to get from A to B.

From A to B we go 6 along and 4 down.
We can find the midpoint by halving the distance.

6 ÷ 2 = 3 and 4 ÷ 2 = 2
The midpoint is 3 along and 2 down from A.

The midpoint is at (-1, 1)

Try this:

Find the midpoint of AB.

## Vertical and Horizontal Lines

On the grid we have a line.

The line runs along all of the points where y = 2.

Every point on the line has a y coordinate of 2.

The line is called y = 2

Here is another line

The line runs along all of the points where x = -3

Every point on the line has a x coordinate of -3

The equation of the line is x = -3

Try these:

Find the equation of the line:

Find the equation of the line: