# 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?

### Comment

The x co-ordinate is shown first.

### Answer

*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 this game [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] . 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.

### Answer

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.

11.3.1 Plotting Points