Lesson 12Interpreting Points on a Coordinate Plane

Learning Goal

Let’s examine what points on the coordinate plane can tell us.

Learning Targets

I can explain how rational numbers represent balances in a money context.
I can explain what points in a four-quadrant coordinate plane represent in a situation.
I can plot points in a four-quadrant coordinate plane to represent situations and solve problems.

Warm Up: Unlabeled Points

Label each point on the coordinate plane with the appropriate letter and ordered pair.

$A = (7, - 5.5)$

$B = (- 8, 4)$

$C = (3, 2)$

$D = (- 3.5, 0.2)$

A coordinate grid extending from -10 to 10 in both the horizontal and vertical directions with 4 points plotted.

Activity 1: Account Balance

The graph shows the balance in a bank account over a period of 14 days. The axis labeled $b$ represents account balance in dollars. The axis labeled $d$ represents the day.

A graph with 14 points. A horizontal axis d, going from 0 to 14 in increments of 1. A vertical axis b, going from -150 to 400 in increments of 50.

Estimate the greatest account balance. On which day did it occur?
Estimate the least account balance. On which day did it occur?
What does the point $(6, - 50)$ tell you about the account balance?
How can we interpret $| - 50 |$ in the context?

Activity 2: High and Low Temperatures

The coordinate plane shows the high and low temperatures in Nome, Alaska over a period of 8 days. The axis labeled $T$ represents temperatures in degrees Fahrenheit. The axis labeled $d$ represents the day.

A graph of 16 points plotted on a coordinate plane with the origin labeled "O." The numbers 1 through 9 are indicated on the the d axis. The numbers negative 6 through 28, in increments of 2, are indicated on the T axis. The data points are presented in the following 8 groups. Group 1. 1 comma 28 and 1 comma 26. Group 2. 2 comma 26 and 2 comma 20. Group 3. 3 comma 21 and 3 comma 11. Group 4. 4 comma 11 and 4 comma 3. Group 5. 5 comma 13 and 5 comma 10. Group 6. 6 comma 17 and 7 comma 7. Group 7. 7 comma 7 and 7 comma negative 3. Group 8. 8 comma 2 and 8 comma negative 1.

Problem 1

What was the warmest high temperature?
What was the coldest high temperature?
Write an inequality to compare the warmest and coldest high temperatures.

Problem 2

What was the coldest low temperature?
What was the warmest low temperature?
Write an inequality to compare the warmest and coldest low temperatures.

Problem 3

On which day(s) did the largest difference between the high and low temperatures occur? Write down this difference.
On which day(s) did the smallest difference between the high and low temperatures occur? Write down this difference.

Are you ready for more?

To get from the point $(2, 1)$ to $(- 4, 3)$ , 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.

An unlabeled coordinate grid with points at (2, 1) and (-4, 3). A vertical line goes up from (2, 1) and connects to a horizontal line drawn from (-4, 3).

Problem 1

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?

Problem 2

The point $(0, 3)$ is 4 taxicab units away from $(- 4, 3)$ and 4 taxicab units away from $(2, 1)$ .

Find as many other points as you can that are 4 taxicab units away from both $(- 4, 3)$ and $(2, 1)$ .
Are there any points that are 3 taxicab units away from both points?

Lesson Summary

Points on the coordinate plane can give us information about a context or a situation. One of those contexts is about money.

To open a bank account, we have to put money into the account. The account balance is the amount of money in the account at any given time. If we put in $350 when opening the account, then the account balance will be 350.

Sometimes we may have no money in the account and need to borrow money from the bank. In that situation, the account balance would have a negative value. If we borrow $200, then the account balance is -200.

A coordinate grid can be used to display both the balance and the day or time for any balance. This allows to see how the balance changes over time or to compare the balances of different days.

Similarly, if we plot on the coordinate plane data such as temperature over time, we can see how temperature changes over time or compare temperatures of different times.