# How to Figure out X & Y Coordinates

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In mathematics, sometimes you are asked to work out the x and y coordinates for a point or line drawn on a graph. Usually these questions show a pair of numbered x-and y-axes. The x-axis is the horizontal line, and the y-axis is the vertical line. The numbers on the axes need to be equally spaced the axes should meet at zero. Even when there are few numbers labelled on the axes, finding the x and y coordinates is relatively easy.

### Things You'll Need

• Calculator
• Ruler
• Find the point on the graph in which you are interested; in many questions this will be marked on the graph for you.

• Draw a vertical line down from the point to where it crosses the horizontal x-axis.

• Calculate the point where the vertical line crosses the x-axis and label it "x." This is the x-coordinate. If there is no number labeled on the x-axis at this point, you will need to work it out.

• Measure with a ruler the distance from zero to x. This could be any length, but for an example let's say the distance was 2 centimeters.

• Measure with a ruler from zero to the next biggest point on the x-axis that has been labelled. To continue with the example, say that the mark is 3 centimeters from zero to on the x axis.

• Write these two measurements as a fraction, with the short length (indicating x) divided by longer length, the next mark on the asix. In the example, you would write "2cm / 3cm."

• Note the label of the mark of the second, longer point to which you measured, and designate the fraction as equal to the x-coordinate divided by the value of the label.

In the example, say that the value of the label next to the crossing point was 6; you would write "2cm/ 3cm = x / 6."

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• Simplify the equation so that only x remains on one side to find the x value; you can do the calculation in your head or use a calculator:

2cm/3cm = x/6

6 (2/3cm) = x

4 cm = x

Therefore your x value in the example is 4

• Repeat all of these stages to find the y-coordinate, but start by drawing a horizontal line from the point of interest to the vertical y-axis.

• Write your coordinates in the standard format; that is, inside a pair of brackets and separated by a comma. The x-coordinate always comes first.

For example, write "(4, 10)" if x=4 and y=10.

## References

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