11.3.1 Plotting Points
Many graphs and charts are constructed by plotting points on a grid.
The graph below shows two perpendicular lines: the horizontal axis and the vertical axis, which set up a grid. Each axis is marked with a scale, in this case from 0 to 3. The point where the two axes meet and where the value on both scales is zero is known as the origin. (Axes is the plural form of axis.)
We can describe the location of any point on the grid by its horizontal and vertical distance from the origin. In the graph below, the horizontal axis has been labeled with an “x” and the vertical axis with a “y.” This is because the horizontal axis is usually known as the x-axis and the vertical axis as the y-axis.
Look at the point P in the above graph. To get to the point P from the origin, move 3 units across and 2 units up. (Alternatively, the point P is opposite 3 on the x-axis and 2 on the y-axis.) We say that P has the coordinates (3, 2).
The horizontal distance of P from the origin is known as the x-coordinate of P and the vertical distance from the origin is known as the y-coordinate of P. So for point P, 3 is the x-coordinate and 2 is the y-coordinate.
Notice that the x-coordinate is the first coordinate in the pair and the y-coordinate is the second coordinate in the pair. So the general form for the coordinates of a point is (x, y). This is important to remember to avoid plotting points the wrong way round!
In the same way, Q is 1 unit across and 3 units up, so Q has coordinates (1, 3).