Section 3.6 The Rectangular Coordinate System
We will use two number lines in order to get a picture of our equations!
Vocabulary:
x-axis:
y-axis:
origin:
Cartesian Coordinate System = Rectangular Coordinate System
Plotting Points: If we know values for x and y, we can write them as an
Ordered Pair (x, y) (notice that this is in alphabetical order!)
So (2, 5) is not the same point as (5, 2). Be Careful!!
To plot the point (2, 5) we have two steps:
1. Draw a vertical line through 2 on the x-axis
2. Draw a horizontal line through 5 on the y-axis
3. Draw the point (2, 5) where these two lines intersect.
Now we have "plotted the point" (2, 5) and that point is called the
"graph" of (2, 5).
We say that 2 is the x-coordinate of the point and that 5 is the
y-coordinate of the point.
We could also plot the point (2, 5) by thinking :
1. First move 2 units in the positive direction on the x-axis (right).
2. Then move 5 units in the positive direction on the y-axis (up).
3. Plot the point. Label the point on the graph.
Get some graph paper and plot the following points. Be sure to label them!
a. P(2, ­3)
b. Q(­3, 5)
c. R(8, 4)
d. S(­4, ­2)
The Quadrants of the Rectangular Coordinate System are labeled with Roman Numerals in a counterclockwise order. We start with Quadrant I where both x and y values are positive:
Refer to the points you just plotted. In which Quadrant does each point lie?
a. P(2, ­3)
b. Q(­3, 5)
c. R(8, 4)
d. S(­4, ­2)
The Scale of a Graph: The tick marks on a grid may represent 1 unit
each, but they could also represent 2, 5, 10, 100,...or any number we
choose!
It is your responsibility to label your graph so that anyone can clearly
determine the scale you are using.
Refer to our book on pages 289-291...
Work together with a partner or small group to create an appropriate graph for the Your Turn 3 problem on page 292.
Graphing and Geometry: Sometimes when we connect the points we
have plotted with straight line segments, we get a geometrical shape.
Then we can use our grid to find the perimeter and area of the shape!
EXAMPLE: Plot the given points and connect them to form a
triangle. Use the graph to find the area of the triangle.
A(-2, 1)
B(2, 5)
C(4, 1)
EXAMPLE: Plot the following points and connect them in order by using line segments. Use the graph to find the area of the geometric shape.
A(­3, ­1)
B(­3, 2)
C(­1, 3)
D(2, 2)
E(2, ­1)