# Transformation: Coordinates

## We use Coordinates to allow us to pinpoint an exact location on a graph or a map. Coordinates are pairs of numbers that identify how far along (on the horizontal, X axis) and how far up (on the vertical,Y axis) the point is located.

Coordinates are written in brackets and are separated by a comma. The first number is the X coordinate (along) and the second number is the Y coordinate (up). There are many ways of remembering this - imagine a plane taking off, along the runway and then up into the air or walking into your house and going along a corridor and then up the stairs.

The best way to explain this is to look at an example: When working out the position of a point we begin at the 'Origin' - this is where the X and Y axes intersect, at zero.

Consider point A, first we look at its position on the X axis, how far along the X axis from the origin ... 1, this is the X coordinate. Then we look at its position on the Y axis, how far up the Y axis from the origin ... 0, this is the Y coordinate.

The coordinates of point A are (1,0)

Consider point B, first we look at its position on the X axis, how far along the X axis from the origin ... 0, this is the X coordinate. Then we look at its position on the Y axis, how far up the Y axis from the origin ... 2, this is the Y coordinate.

The coordinates of point B are (0,2)

Consider point C, first we look at its position on the X axis, how far along the X axis from the origin ... 2, this is the X coordinate. Then we look at its position on the Y axis, how far up the Y axis from the origin ... 5, this is the Y coordinate. The coordinates of point C are (1,0)

Where on the diagram is coordinates (5,4)?

Begin at the origin - move along the X axis 5 (because the X coordinate is 5). From this position, move up the Y axis 4 (because the Y coordinate is 4). The point that you reach will be at coordinates (5,4) which is point D. To put it simply - start at the origin, along 5 then up 4.

Where on the diagram is coordinates (3,2)?

Begin at the origin - move along the X axis 3 (because the X coordinate is 3). From this position, move up the Y axis 2 (because the Y coordinate is 2). The point that you reach will be at coordinates (3,2) which is point E. To put it simply - start at the origin, along 3 then up 2.

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### Now we will move to a grid with four quadrants in which the X and Y axes have negative and positive numbers. The 'Origin' is still the point where the X and Y axes intersect, at zero, but it is now in the centre of the grid. Think of this grid as being divided into four quadrants.
The top right quadrant has values positive X and Y coordinates. The top left quadrant has positive Y and negative X coordinates. The bottom left has negative X and Y coordinates. The bottom right has positive X and negative Y coordinates.

When working out the position of a point we still begin at the 'Origin' - this is where the X and Y axes intersect, at zero. Now in the centre of the grid.

Consider point A, first we look at its position on the X axis, how far along the X axis from the origin ... 5, this is the X coordinate. Then we look at its position on the Y axis, how far up the Y axis from the origin ... 4, this is the Y coordinate.

The coordinates of point A are (5,4)

Consider point B, first we look at its position on the X axis, how far along the X axis from the origin ... -3, this is the X coordinate. Then we look at its position on the Y axis, how far up the Y axis from the origin ... 4, this is the Y coordinate.

The coordinates of point B are (-3,4)

Consider point C, first we look at its position on the X axis, how far along the X axis from the origin ... 3, this is the X coordinate. Then we look at its position on the Y axis, how far up (or down) the Y axis from the origin ... 4, this is the Y coordinate.

The coordinates of point C are (3,-4)

Where on the diagram is coordinates (-4,-3)?

Begin at the origin - move along the X axis -4 (because the X coordinate is -4). From this position, move down the Y axis -3 (because the Y coordinate is -3). The point that you reach will be at coordinates (-4,-3) which is point D. To put it simply - start at the origin, move left 4 (because it is negative) then down 3 (because it is negative).

Where on the diagram is coordinates (-2,1)?

Begin at the origin - move along the X axis -2 (because the X coordinate is -2). From this position, move up the Y axis 1 (because the Y coordinate is 1). The point that you reach will be at coordinates (-2,1) which is point E. To put it simply - start at the origin, move left 2 (because it is negative) then up 1 (because it is positive).

What are the coordinates of point F?

You should get (1,-2) ..... along 1 and then down 2

## Remember - The X coordinate and then the Y coordinate.

### along a corridor and then up the stairs

This Coordinate Archery game from Maths is Fun is excellent to practice finding coordinates - start at beginner level with only one quadrant and then move up the levels until you are using all four quadrants.

Practice working with Coordinates with these worksheets from Primary Resources

Anthony Browne Character Mask Using Coordinates