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).

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This shows a set of axes with the scales marked from minus 3 to 3 on both the horizontal x-axis and the vertical y-axis. The axes intersect at the origin. Four points A, B, C, and D are marked. A is opposite 3 on the x-axis and opposite 1 on the y-axis. B is opposite minus 3 on the x-axis and opposite 1 on the y-axis. C is opposite minus 2 on the x-axis and opposite minus 2 on the y-axis. D is opposite 2 on the x-axis and opposite minus 1 on the y-axis.

Solution symbolActivity: Reading Coordinates

Write down the coordinates of points A, C, and D, shown in the graph above. What are the coordinates of the origin?

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The x co-ordinate is shown first.

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Answer

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This shows a set of axes with the scales marked from minus 3 to 3 on both the horizontal x-axis and the vertical y-axis. The axes intersect at the origin. Four points A, B, C, and D are marked. A is opposite 3 on the x-axis and opposite 1 on the y-axis and is labelled A(3,1). B is opposite minus 3 on the x-axis and opposite 1 on the y-axis and is labelled B(minus 3, 1). C is opposite minus 2 on the x-axis and opposite minus 2 on the y-axis and is labelled C(minus 2, minus 2). D is opposite 2 on the x-axis and opposite minus 1 on the y-axis and is labelled D(2, minus 1).

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).

Videoclip iconFor 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.

Solution symbolActivity: 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).

Solution symbolIt 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.

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This shows a set of axes with the scales marked from –3 to 3 on both the horizontal x-axis and the vertical y-axis. The axes intersect at the origin. Four points E, F, G, and H are marked. E is opposite 1 on the x-axis and opposite 1 on the y-axis and is labelled E (1, 1). F is opposite minus 2 on the x-axis and opposite minus 1 on the y-axis and is labelled F (minus 2, minus 1). G is opposite 1 on the x-axis and opposite minus 3 on the y-axis. H is opposite minus 2 on the x-axis and opposite 3 on the y-axis.

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.

Videoclip iconNow try the game again, but choose “hard” as the level and you can plot your own points.

11.3.1 Plotting Points

11.3.3 Decimal Coordinates