1. 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.

2. 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 x 5 -4 -2 1 3 -5 -1 4 -3 2

3. The horizontal number line is called the ______.
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2 O

4. The horizontal number line is called the ______. x-axis
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-axis O

5. The horizontal number line is called the ______. x-axis
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-axis
The vertical number line is called the ______. O

6. The horizontal number line is called the ______. x-axis
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-axis
The vertical number line is called the ______.
y-axis O

7. The horizontal number line is called the ______. x-axis
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-axis
The vertical number line is called the ______.
y-axis O
The point of intersection of the two axes is called the _____.

8. The horizontal number line is called the ______. x-axis
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-axis
The vertical number line is called the ______.
y-axis O
The point of intersection of the two axes is called the _____.
origin

9. The horizontal number line is called the ______. x-axis
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-axis
The vertical number line is called the ______.
y-axis
The point of intersection of the two axes is called the _____.
origin
The two axes separate the plane into four regions called _________.

10. The horizontal number line is called the ______. x-axis
The Coordinate Plane
The horizontal number line is called the ______. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-axis
Quadrant II
(–, +)
Quadrant I
(+, +)
The vertical number line is called the ______.
y-axis
The point of intersection of the two axes is called the _____.
Quadrant III
(–, –)
Quadrant IV
(+, –)
origin
The two axes separate the plane into four regions called _________.
quadrants

11. The Coordinate Plane
An ordered pair of real numbers, called coordinates of a point, locates a point in the coordinate plane.

12. 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.

13. 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.
one point

14. 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.
one point
The point in the coordinate plane is called the graph of the ordered pair.

15. 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.
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.

16. 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.
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

17. Completeness Property for Points in the 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.
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 __________________________.

18. Completeness Property for Points in the 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.
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

19. Completeness Property for Points in the 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.
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

20. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
It tells the number of units the point lies to the __________ of the origin.

21. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
It tells the number of units the point lies to the __________ of the origin.
left or right

22. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
It tells the number of units the point lies to the __________ of the origin.
left or right
The second number, 3, is called the
___________.
y-coordinate
It tells the number of units the point lies _____________ the origin.

23. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
(4, 3)
It tells the number of units the point lies to the __________ of the origin.
left or right
The second number, 3, is called the
___________.
y-coordinate
It tells the number of units the point lies _____________ the origin.
above or below

24. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
(4, 3)
It tells the number of units the point lies to the __________ of the origin.
left or right
The second number, 3, is called the
___________.
y-coordinate
It tells the number of units the point lies _____________ the origin.
above or below
What is the coordinate of the origin?

25. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point A at (4, 3)
The first number, 4, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
(4, 3)
It tells the number of units the point lies to the __________ of the origin.
left or right
(0, 0)
The second number, 3, is called the
___________.
y-coordinate
It tells the number of units the point lies _____________ the origin.
above or below
What is the coordinate of the origin?

26. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3) y x 5 -4 -2 1 3 -5 -1 4 -3 2

27. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
It tells the number of units the point lies to the __________ of the origin.

28. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
It tells the number of units the point lies to the __________ of the origin.
left or right

29. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
It tells the number of units the point lies to the __________ of the origin.
left or right
The second number, –3, is called the
___________.
y-coordinate
It tells the number of units the point lies _____________ the origin.

30. Graphing an ordered pair, (point): (x, y)
The Coordinate Plane
Graphing an ordered pair, (point): (x, y)
Graph point B at (2, –3)
The first number, 2, is called the
___________. y x 5 -4 -2 1 3 -5 -1 4 -3 2
x-coordinate
It tells the number of units the point lies to the __________ of the origin.
left or right
The second number, –3, is called the
___________.
y-coordinate
(2, –3)
It tells the number of units the point lies _____________ the origin.
above or below

31. Give the coordinates of the points A, B, C, & D
The Coordinate Plane
Give the coordinates of the points A, B, C, & D y x 5 -4 -2 1 3 -5 -1 4 -3 2
Point A(x, y) = B B A A
Point B(x, y) =
Point C(x, y) =
Point D(x, y) = C C D D

32. Name the points A, B, C, & D Point A(x, y) = (3, 2) B B A A
The Coordinate Plane
Name the points A, B, C, & D y x 5 -4 -2 1 3 -5 -1 4 -3 2
Point A(x, y) =
(3, 2)
(–3, 2) B B
(3, 2) A A
Point B(x, y) =
(–3, 2)
Point C(x, y) =
(–3, –2)
Point D(x, y) =
(3, –2)
(–3, –2) C C D
(3, –2) D

33. The Coordinate Plane
On a piece of grid paper draw lines representing the x-axis and the y-axis. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)

34. Consider these questions:
The Coordinate Plane
On a piece of grid paper draw lines representing the x-axis and the y-axis. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
x = 2
1) What do you notice about the graphs of these points?

35. Consider these questions:
The Coordinate Plane
On a piece of grid paper draw lines representing the x-axis and the y-axis. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
x = 2
1) What do you notice about the graphs of these points?
They lie on a vertical line.

36. Consider these questions:
The Coordinate Plane
On a piece of grid paper draw lines representing the x-axis and the y-axis. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
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?

37. Consider these questions:
The Coordinate Plane
On a piece of grid paper draw lines representing the x-axis and the y-axis. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
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.

38. The Coordinate Plane
On a piece of grid paper draw lines representing the x-axis and the y-axis. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Write a general statement about ordered pairs that have the same x-coordinate.

39. The Coordinate Plane
On a piece of grid paper draw lines representing the x-axis and the y-axis. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
x = 2
Write a general statement about ordered pairs that have the same x-coordinate.

40. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)

41. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)

42. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
1) What do you notice about the graphs of these points?

43. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
1) What do you notice about the graphs of these points?
They lie on a horizontal line.

44. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
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?

45. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Consider these questions:
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.

46. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
Write a general statement about ordered pairs that have the same y-coordinate.

47. On the same coordinate plane
The Coordinate Plane
On the same coordinate plane y x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph :
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)
y = – 4
Write a general statement about ordered pairs that have the same y-coordinate.

48. If a and b are real numbers,
The 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 _____

49. If a and b are real numbers,
The 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

50. If a and b are real numbers,
The 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 x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph the lines: x = –3

51. If a and b are real numbers,
The 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 x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph the lines: x = –3

52. If a and b are real numbers,
The 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 x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph the lines: x = –3
y = 2

53. If a and b are real numbers,
The 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 x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph the lines: x = –3
y = 2

54. If a and b are real numbers,
The 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 x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph the lines: x = –3
y = 2
Graph the point of intersection of these lines.

55. If a and b are real numbers,
The 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 x 5 -4 -2 1 3 -5 -1 4 -3 2
Graph the lines: x = –3
y = 2
(–3, 2)
Graph the point of intersection of these lines.

56. The Coordinate Plane
End of Lesson