Transcript The Coordinate Plane

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