# Lesson 12

Constructing the Coordinate Plane

Let’s investigate different ways of creating a coordinate plane.

### Problem 1

Draw and label an appropriate pair of axes and plot the points.

$$(\frac15, \frac45)$$

$$(\text{-}\frac {3}{5}, \frac25)$$

$$(\text-1 \frac15, \text{-}\frac {4}{5})$$

$$(\frac15, \text{-}\frac {3}{5})$$

### Problem 2

Diego was asked to plot these points: $$(\text-50, 0)$$, $$(150, 100)$$, $$(200, \text-100)$$, $$(350, 50)$$, $$(\text-250, 0)$$. What interval could he use for each axis? Explain your reasoning.

### Problem 3

1. Name 4 points that would form a square with the origin at its center.
2. Graph these points to check if they form a square.

### Problem 4

Which of the following changes would you represent using a negative number? Explain what a positive number would represent in that situation.

1. A loss of 4 points
2. A gain of 50 yards
3. A loss of $10 4. An elevation above sea level (From Unit 7, Lesson 5.) ### Problem 5 Jada is buying notebooks for school. The cost of each notebook is$1.75.

1. Write an equation that shows the cost of Jada’s notebooks, $$c$$, in terms of the number of notebooks, $$n$$, that she buys.
2. Which of the following could be points on the graph of your equation?

$$(1.75, 1)$$

$$(2, 3.50)$$

$$(5, 8.75)$$

$$(17.50, 10)$$

$$(9, 15.35)$$

(From Unit 6, Lesson 16.)

### Problem 6

A corn field has an area of 28.6 acres. It requires about 15,000,000 gallons of water. About how many gallons of water per acre is that?

A:

5,000

B:

50,000

C:

500,000

D:

5,000,000

(From Unit 5, Lesson 13.)