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
- Name 4 points that would form a square with the origin at its center.
- 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.
- A loss of 4 points
- A gain of 50 yards
- A loss of $10
- An elevation above sea level
Problem 5
Jada is buying notebooks for school. The cost of each notebook is $1.75.
- Write an equation that shows the cost of Jada’s notebooks, \(c\), in terms of the number of notebooks, \(n\), that she buys.
-
Which of the following could be points on the graph of your equation?
\((1.75, 1)\)
\((2, 3.50)\)
\((5, 8.75)\)
\((17.50, 10)\)
\((9, 15.35)\)
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?
5,000
50,000
500,000
5,000,000