Transcript The Coordinate Plane

The Coordinate
Plane
Section 6.8
The Coordinate Plane
A coordinate plane is formed by the
intersection of a horizontal number line
called the x-axis and a vertical number
line called the y-axis. The axes meet at
a point called the origin and divide the
coordinate plane into four quadrants.
Points in a coordinate plane are represented by ordered pairs. The first
number is the x-coordinate. The second number is the y-coordinate.
Point P above is represented by the ordered pair (–2, 1).
x-coordinate
P(–2, 1)
y-coordinate
The Coordinate Plane
Naming Points in a Coordinate Plane
Give the coordinates of the points.
C
A (3, 1)
A
B
SOLUTION
Point A is 3 units to the right of the origin
and 1 unit up.
So, the x-coordinate is 3 and the y-coordinate is 1.
The coordinates of A are (3, 1).
The Coordinate Plane
Naming Points in a Coordinate Plane
Give the coordinates of the points.
C
A
A (3, 1)
B
SOLUTION
B
(–3, –2)
Point B is 3 units to the left of the origin
and 2 units down.
So, the x-coordinate is –3 and the y-coordinate is –2.
The coordinates of B are (–3, –2).
The Coordinate Plane
EXAMPLE
1
Naming Points in a Coordinate Plane
Give the coordinates of the points.
A
B
C (0, 2)
A (3, 1)
C
SOLUTION
B
(–3, –2)
Point C is 2 units up from the origin.
So, the x-coordinate is 0 and the y-coordinate is 2.
The coordinates of C are (0, 2).
The Coordinate Plane
Graphing Points in a Coordinate Plane
Plot the point and describe its location.
A(4, –2)
4
–2
SOLUTION
Begin at the origin, move 4 units to the right
then 2 units down. Point A lies in Quadrant IV.
A (4, –2)
The Coordinate Plane
Graphing Points in a Coordinate Plane
Plot the point and describe its location.
(–1, 2) B
A(4, –2)
B(–1, 2)
2
4
-1
SOLUTION
Begin at the origin, move 4 units to the right
then 2 units down. Point A lies in Quadrant IV.
Begin at the origin, move 1 unit to the left
then 2 units up. Point B lies in Quadrant II.
–2
A (4, –2)
The Coordinate Plane
Graphing Points in a Coordinate Plane
Plot the point and describe its location.
(–1, 2) B
A(4, –2)
B(–1, 2)
C(0, –3)
2
4
-1
SOLUTION
–3
–2
A (4, –2)
C (0, –3)
Begin at the origin, move 4 units to the right
then 2 units down. Point A lies in Quadrant IV.
Begin at the origin, move 1 unit to the left
then 2 units up. Point B lies in Quadrant II.
Begin at the origin, move 3 units down. Point C lies on the y-axis.
The Coordinate Plane
Finding Perimeter
Identify the figure and find its perimeter.
SOLUTION
Points A, B, C, and D form a
rectangle.
To find the length l, find the
horizontal distance from A to B.
l = | x-coordinate of A – x-coordinate of B |
= | –32 – 32 | = | –64 | = 64
The Coordinate Plane
Finding Perimeter
Identify the figure and find its perimeter.
SOLUTION
Points A, B, C, and D form a
rectangle.
To find the length l, find the
horizontal distance from A to B.
To find the width w, find the
vertical distance from A to D.
l = | x-coordinate of A –
x-coordinate of B |
w = | y-coordinate of A – y-coordinate of D |
= | –32 – 32 | = | –64 | = 64
= | 24 – (– 24) | = | 48 | = 48
The Coordinate Plane
Finding Perimeter
Identify the figure and find its perimeter.
SOLUTION
Points A, B, C, and D form a
rectangle.
To find the length l, find the
horizontal distance from A to B.
To find the width w, find the
vertical distance from A to D.
l = | x-coordinate of A –
x-coordinate of B |
w = | y-coordinate of A –
y-coordinate of D |
= | –32 – 32 | = | –64 | = 64
= | 24 – (– 24) | = | 48 | = 48
Perimeter = 2l + 2w = 2(64) + 2(48) = 224
ANSWER
The rectangle has a perimeter of 224 units.
Notebook
The Coordinate Plane
• (4,5)
– First number represents the x value
– Second number represents the y value
• How to plot a point
– Start at zero
– Go over (right or left) the number of spaces as the first
number
– From that point, go up or down the number of spaces as the
second number
– Mark with a point.
• How to give a point a coordinate
– Follow the point straight down, that is your x value
– Follow the point straight across, that is your y value
– Put the numbers in (x,y) format