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The Coordinate Plane. What You'll Learn. You will learn to name and graph ordered pairs on a coordinate plane. In coordinate geometry, grid paper is used to locate points. The plane of the grid is called the coordinate plane. y. 5. 5. 4. 3. 2. 1. x. -5. -5. -4. -3. -2. -1. 1. - PowerPoint PPT Presentation
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The Coordinate PlaneThe Coordinate Plane
You will learn to name and graph ordered pairs on acoordinate plane.
In coordinate geometry, grid paper is used to locate points.
The plane of the grid is called the coordinate plane.
The Coordinate PlaneThe Coordinate Plane
You will learn to name and graph ordered pairs on acoordinate plane.
In coordinate geometry, grid paper is used to locate points.
The plane of the grid is called the coordinate plane.
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.
O
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
O
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
The vertical number lineis called the ______.
O
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
The vertical number lineis called the ______.y-axis
O
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
The vertical number lineis called the ______.y-axis
O
The point of intersection of the twoaxes is called the _____.
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
The vertical number lineis called the ______.y-axis
O
The point of intersection of the twoaxes is called the _____.origin
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
The vertical number lineis called the ______.y-axis
The point of intersection of the twoaxes is called the _____.origin
The two axes separate the plane intofour regions called _________.
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The horizontal number lineis called the ______.x-axis
The vertical number lineis called the ______.y-axis
The point of intersection of the twoaxes is called the _____.origin
The two axes separate the plane intofour regions called _________.quadrants
Quadrant I(+, +)
Quadrant II
(–, +)
Quadrant III
(–, –)
Quadrant IV
(+, –)
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
one point
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
one point
The point in the coordinate plane is called the graph of the ordered pair.
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
one point
The point in the coordinate plane is called the graph of the ordered pair.
Locating a point on the coordinate plane is called _______ the ordered pair.
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
one point
The point in the coordinate plane is called the graph of the ordered pair.
Locating a point on the coordinate plane is called _______ the ordered pair.graphing
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
one point
The point in the coordinate plane is called the graph of the ordered pair.
Locating a point on the coordinate plane is called _______ the ordered pair.graphing
Postulate 2 – 4
Completeness Property for Points
in the Plane
Each point in a coordinate plane corresponds to exactly one __________________________.
Each ordered pair of real numbers corresponds to exactly one __________________________.
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
one point
The point in the coordinate plane is called the graph of the ordered pair.
Locating a point on the coordinate plane is called _______ the ordered pair.graphing
Postulate 2 – 4
Completeness Property for Points
in the Plane
Each point in a coordinate plane corresponds to exactly one __________________________.
Each ordered pair of real numbers corresponds to exactly one __________________________.
ordered pair of real numbers
The Coordinate PlaneThe Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates apoint in the coordinate plane.
Each ordered pair corresponds to EXACTLY ________ in the coordinate plane.
one point
The point in the coordinate plane is called the graph of the ordered pair.
Locating a point on the coordinate plane is called _______ the ordered pair.graphing
Postulate 2 – 4
Completeness Property for Points
in the Plane
Each point in a coordinate plane corresponds to exactly one __________________________.
Each ordered pair of real numbers corresponds to exactly one __________________________.
ordered pair of real numbers
point in the coordinate plane
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.left or right
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The second number, 3, is called the___________.y-coordinate
It tells the number of units the point lies _____________ the origin.
left or right
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The second number, 3, is called the___________.y-coordinate
It tells the number of units the point lies _____________ the origin.
left or right
above or below
(4, 3)
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The second number, 3, is called the___________.y-coordinate
It tells the number of units the point lies _____________ the origin.
left or right
above or below
(4, 3)
What is the coordinate of the origin?
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The second number, 3, is called the___________.y-coordinate
It tells the number of units the point lies _____________ the origin.
left or right
above or below
(4, 3)
What is the coordinate of the origin?
(0, 0)
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.left or right
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The second number, –3, is called the___________.y-coordinate
It tells the number of units the point lies _____________ the origin.
left or right
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the___________.x-coordinate
It tells the number of units the point lies tothe __________ of the origin.
The second number, –3, is called the___________.y-coordinate
It tells the number of units the point lies _____________ the origin.
left or right
above or below
(2, –3)
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Give the coordinates of the points A, B, C, & D
Point A(x, y) =
Point B(x, y) =
Point C(x, y) =
Point D(x, y) =
AB
C D
A
DC
B
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Name the points A, B, C, & D
Point A(x, y) =
Point B(x, y) =
Point C(x, y) =
Point D(x, y) =
A(3, 2) (–3, 2) B
(–3, –2)C (3, –2)D
(3, 2)A
DC
B
(–3, –2)
(–3, 2)
(3, –2)
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Point A(x, y) = A(2, 4)
Point B(x, y) = B(2, 0)
Point C(x, y) = C(2, –3)
Point D(x, y) = D(2, –5)
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Consider these questions:
Point A(x, y) = A(2, 4)
Point B(x, y) = B(2, 0)
Point C(x, y) = C(2, –3)
Point D(x, y) = D(2, –5)
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
1) What do you notice about the graphs of these points?
x = 2
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Consider these questions:
Point A(x, y) = A(2, 4)
Point B(x, y) = B(2, 0)
Point C(x, y) = C(2, –3)
Point D(x, y) = D(2, –5)
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
1) What do you notice about the graphs of these points?
They lie on a vertical line.
x = 2
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Consider these questions:
Point A(x, y) = A(2, 4)
Point B(x, y) = B(2, 0)
Point C(x, y) = C(2, –3)
Point D(x, y) = D(2, –5)
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
1) What do you notice about the graphs of these points?
They lie on a vertical line.
2) What do you notice about the x-coordinates of these points?
x = 2
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Consider these questions:
Point A(x, y) = A(2, 4)
Point B(x, y) = B(2, 0)
Point C(x, y) = C(2, –3)
Point D(x, y) = D(2, –5)
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
1) What do you notice about the graphs of these points?
They lie on a vertical line.
2) What do you notice about the x-coordinates of these points?
They are the same number.
x = 2
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Point A(x, y) = A(2, 4)
Point B(x, y) = B(2, 0)
Point C(x, y) = C(2, –3)
Point D(x, y) = D(2, –5)
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
Write a general statement about ordered pairs that have the same x-coordinate.
The Coordinate PlaneThe Coordinate Plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Point A(x, y) = A(2, 4)
Point B(x, y) = B(2, 0)
Point C(x, y) = C(2, –3)
Point D(x, y) = D(2, –5)
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
Write a general statement about ordered pairs that have the same x-coordinate.
x = 2
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
On the same coordinate plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
On the same coordinate plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Consider these questions:
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
1) What do you notice about the graphs of these points?
On the same coordinate plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Consider these questions:
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
1) What do you notice about the graphs of these points?
They lie on a horizontal line.
On the same coordinate plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Consider these questions:
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
1) What do you notice about the graphs of these points?
They lie on a horizontal line.
2) What do you notice about the y-coordinates of these points?
On the same coordinate plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Consider these questions:
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
1) What do you notice about the graphs of these points?
They lie on a horizontal line.
2) What do you notice about the y-coordinates of these points?
They are the same number.
On the same coordinate plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
Write a general statement about ordered pairs that have the same y-coordinate.
On the same coordinate plane
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
The Coordinate PlaneThe Coordinate Plane
Point W(x, y) = W(–4, –4)
Point X(x, y) = X(–2, –4)
Point Y(x, y) = Y(0, –4)
Point Z(x, y) = Z(3, –4)
Graph :
Write a general statement about ordered pairs that have the same y-coordinate.
y = – 4
On the same coordinate plane
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
x = a
y = b
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
x = a
y = b
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graph the lines: x = –3
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
x = a
y = b
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graph the lines: x = –3
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
x = a
y = b
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graph the lines: x = –3
y = 2
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
x = a
y = b
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graph the lines: x = –3
y = 2
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
x = a
y = b
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graph the lines: x = –3
y = 2
Graph the point of intersection of theselines.
The Coordinate PlaneThe Coordinate Plane
Theorem 2 – 4
If a and b are real numbers,
a vertical line contains all points (x, y) such that _____
and
a horizontal line contains all points (x, y) such that _____
x = a
y = b
y
x5-4 -2 1 3 5
5
-4
-2
1
3
5
-5 -1 4
-5
-1
4
-3
-5
2
2-5
-3
Graph the lines: x = –3
y = 2
Graph the point of intersection of theselines.
(–3, 2)
The Coordinate PlaneThe Coordinate Plane
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