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.)