11.3.2 Negative Coordinates
The axes can be extended downward and to the left to include negative values as shown here. In the graph below, B is 3 units to the left of the origin so its x-coordinate is –3. It is 1 unit up, so its y coordinate is 1. So B has coordinates (–3, 1).
Activity: Reading Coordinates
Write down the coordinates of points A, C, and D, shown in the graph above. What are the coordinates of the origin?
The x co-ordinate is shown first.
A is opposite 3 on the x-axis, so its x-coordinate is 3. It is opposite 1 on the y-axis, so its y-coordinate is 1. The coordinates of A are (3, 1).
C is opposite –2 on the x-axis, so its x-coordinate is –2. It is opposite –2 on the y-axis, so its y-coordinate is -2. The coordinates of C are (–2, -2).
The coordinates of D are (2, †1).
The origin has coordinates (0, 0).
For some more fun practice reading plotted points, try . There are three different levels of difficulty to choose from—try medium to start with.
Activity: Plotting Your Own Points
Draw x- and y-axes and mark scales as in the graph above. Mark in the points E at (1, 1), F at (–2, –1), G at (1, –3) and H at (–2, 3).
It would be useful to do this exercise on graph paper as it will be much easier to plot the points if you have a grid to work with. If you have none, you may download a graph paper .PDF file provided in the link below.
The plot you drew should have points in the E, F, G and H marked in the same position they are are shown on the plot above.
E has coordinates (1, 1), so it is plotted 1 unit to the right and 1 unit up, that is, opposite 1 on the x-axis and opposite 1 on the y-axis.
F has coordinates (–2, –1), so F is plotted opposite –2 on the x-axis and opposite –1 on the y-axis.
The coordinates of G are (1, –3) so G is plotted opposite 1 on the x-axis and opposite -3 on the y-axis.
The coordinates of H are (–2, 3) so H is plotted opposite –2 on the x-axis and opposite 3 on the y-axis.
Now try the game again, but choose “hard” as the level and you can plot your own points.