Let’s investigate different ways of creating a coordinate plane.
The following data were collected over one December afternoon in England.
| time after noon (hours) |
temperature ($^\circ \text{C}$) |
|
|---|---|---|
| row 1 | 0 | 5 |
| row 2 | 1 | 3 |
| row 3 | 2 | 4 |
| row 4 | 3 | 2 |
| row 5 | 4 | 1 |
| row 6 | 5 | -2 |
| row 7 | 6 | -3 |
| row 8 | 7 | -4 |
| row 9 | 8 | -4 |
Here are three sets of coordinates. For each set, draw and label an appropriate pair of axes and plot the points.
$(1, 2), (3, \text-4), (\text-5, \text-2), (0, 2.5)$
$(50, 50), (0, 0), (\text-10, \text-30), (\text-35, 40)$
$\left(\frac14, \frac34\right), \left(\frac {\text{-}5}{4}, \frac12\right), \left(\text-1\frac14, \frac {\text{-}3}{4}\right), \left(\frac14, \frac {\text{-}1}{2}\right)$
Discuss with a partner:
Here is a maze on a coordinate plane. The black point in the center is (0, 0). The side of each grid square is 2 units long.
To get from the point $(2,1)$ to $(\text-4,3)$ you can go two units up and six units to the left, for a total distance of eight units. This is called the “taxicab distance,” because a taxi driver would have to drive eight blocks to get between those two points on a map.
Find as many points as you can that have a taxicab distance of eight units away from $(2,1)$. What shape do these points make?
The coordinate plane can be used to show information involving pairs of numbers.
When using the coordinate plane, we should pay close attention to what each axis represents and what scale each uses.
Suppose we want to plot the following data about the temperatures in Minneapolis one evening.
| time (hours from midnight) |
temperature (degrees C) |
|
|---|---|---|
| row 1 | -4 | 3 |
| row 2 | -1 | -2 |
| row 3 | 0 | -4 |
| row 4 | 3 | -8 |
We can decide that the $x$-axis represents number of hours in relation to midnight and the $y$-axis represents temperatures in degrees Celsius.
The data involve whole numbers, so it is appropriate that the each square on the grid represents a whole number.
Here is a graph of the data with the axes labeled appropriately.
On this coordinate plane, the point at $(0, 0)$ means a temperature of 0 degrees Celsius at midnight. The point at $(\text-2, 8)$ means a temperature of 8 degree Celsius at 2 hours before midnight (or 10 p.m.).
