The document discusses key concepts related to coordinate planes and graphing points, including: 1) How to graph points using two perpendicular number lines called axes, with their point of intersection called the origin. 2) How coordinate pairs (x,y) are used to name points, with the first coordinate being the x-coordinate and the second being the y-coordinate. 3) How the axes divide the plane into four quadrants and examples of points in different quadrants. 4) How to find the midpoint between two points by taking the average of their x-coordinates and y-coordinates.

1. Unit 4 - Homework 1
The Coordinate Plane
Domain & Range
Inverse Relation
Finding the Midpoint

2. Coordinate Plane
• To graph, or plot,
points we use two
perpendicular
number lines called
axes.
• The point at which
the axes cross is
called the origin.

3. Coordinate Plane
• To graph, or plot,
points we use two
perpendicular
number lines called
axes.
• The point at which
the axes cross is
called the origin.

4. Coordinate Plane
• To graph, or plot,
points we use two
perpendicular
number lines called
axes.
• The point at which
the axes cross is
called the origin.

5. Coordinate Plane
• To graph, or plot,
points we use two
perpendicular
number lines called
axes.
• The point at which
the axes cross is
called the origin.

6. Coordinate Plane
• To graph, or plot,
points we use two
perpendicular
number lines called
axes.
• The point at which
the axes cross is
called the origin.

7. Coordinate Plane
• Consider the pair
(2, 3). The numbers ( 2, 3)
in such a pair are
called the
coordinates.

8. Coordinate Plane
• Consider the pair x
(2, 3). The numbers ( 2, 3)
in such a pair are
called the
coordinates.
• The first coordinate is
the x-coordinate and

9. Coordinate Plane
• Consider the pair y
(2, 3). The numbers ( 2, 3)
in such a pair are
called the
coordinates.
• The first coordinate is
the x-coordinate and
• the second coordinate
is the y-coordinate.

10. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
point (3, −2) located?
• In which quadrant is the
point (−4, −9) located?

11. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
I
point (3, −2) located?
• In which quadrant is the
point (−4, −9) located?

12. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
II I
point (3, −2) located?
• In which quadrant is the
point (−4, −9) located?

13. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
II I
point (3, −2) located?
• In which quadrant is the
point (−4, −9) located? III

14. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
II I
point (3, −2) located?
• In which quadrant is the
point (−4, −9) located? III IV

15. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
point (3, −2) located?

16. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
point (3, −2) located?
IV

17. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
point (3, −2) located?
• In which quadrant is the
point (−4, −9) located?

18. Quadrants
• The horizontal and
vertical axes divide the
plane into four regions,
or quadrants.
• In which quadrant is the
point (3, −2) located?
• In which quadrant is the
point (−4, −9) located? III

19. Naming Points
• From the point,
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x-
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
is the y-coordinate.

20. Naming Points
• From the point, ( −4, )
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x-
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
is the y-coordinate.

21. Naming Points
• From the point, ( −4, )
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x-
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
(1, )
is the y-coordinate.

22. Naming Points
• From the point, ( −4, )
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x- ( 5, )
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
(1, )
is the y-coordinate.

23. Naming Points
• From the point, ( −4, )
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x- ( 5, )
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
(1, )
is the y-coordinate.

24. Naming Points
• From the point, ( −4, 5 )
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x- ( 5, )
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
(1, )
is the y-coordinate.

25. Naming Points
• From the point, ( −4, 5 )
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x- ( 5, )
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
(1, −4 )
is the y-coordinate.

26. Naming Points
• From the point, ( −4, 5 )
• 1) Trace a vertical line to
find where it crosses the
x-axis. This is the x- ( 5, 0 )
coordinate.
• 2) Trace a horizontal
line to find where it
crosses the y-axis. This
(1, −4 )
is the y-coordinate.

27. Domain & Range
• Domain
( 2, 3)
( −4, 8 )
( −5.7, −3.1)
 5 7
 , 
 2 3

28. Domain & Range
• Domain
• Set of first coordinates of the
function
( 2, 3)
( −4, 8 )
( −5.7, −3.1)
 5 7
 , 
 2 3

29. Domain & Range
• Domain
• Set of first coordinates of the
function
( 2, 3)
( −4, 8 )
( −5.7, −3.1)
 5 7
 , 
 2 3

30. Domain & Range
• Domain
• Set of first coordinates of the
function
( 2, 3)
• {2, -4, -5.7, 5/2} ( −4, 8 )
( −5.7, −3.1)
 5 7
 , 
 2 3

31. Domain & Range
• Domain
• Set of first coordinates of the
function
( 2, 3)
• {2, -4, -5.7, 5/2} ( −4, 8 )
( −5.7, −3.1)
• Range
 5 7
• Set of second coordinates of the  , 
 2 3
function

32. Domain & Range
• Domain
• Set of first coordinates of the
function
( 2, 3)
• {2, -4, -5.7, 5/2} ( −4, 8 )
( −5.7, −3.1)
• Range
 5 7
• Set of second coordinates of the  , 
 2 3
function

33. Domain & Range
• Domain
• Set of first coordinates of the
function
( 2, 3)
• {2, -4, -5.7, 5/2} ( −4, 8 )
( −5.7, −3.1)
• Range
 5 7
• Set of second coordinates of the  , 
 2 3
function
• {3, 8, -3.1, 7/3}

34. Find the domain and range of the function f whose
graph is shown below.
6
5
f 4
3
2
1
-5 -4 -3 -2 -1 1 2 3 4
-1
-2
-3
-4
-5

35. Find the domain and range of the function f whose
graph is shown below.
• Domain 6
5
• {-5, 1, 3, 4} f 4
3
2
1
-5 -4 -3 -2 -1 1 2 3 4
-1
-2
-3
-4
-5

36. Find the domain and range of the function f whose
graph is shown below.
• Domain 6
5
• {-5, 1, 3, 4} f 4
3
• Range
2
• {-5, 0, 1, 3} 1
-5 -4 -3 -2 -1 1 2 3 4
-1
-2
-3
-4
-5

37. Inverse Relation
• The reverse of a relations ordered pair.

38. Inverse Relation
• The reverse of a relations ordered pair.
Relation
x y
3 8
-2 5
0 1
7 -6

39. Inverse Relation
• The reverse of a relations ordered pair.
Relation Inverse Relation
x y y x
3 8 8 3
-2 5 5 -2
0 1 1 0
7 -6 -6 7

40. Midpoint
• What’s the number halfway
between 5 and 14.5?

41. Midpoint
• What’s the number halfway
between 5 and 14.5?
• 9.75 because (5 + 14.5)/2
= 19.5/2 = 9.75

42. Midpoint
• What’s the number halfway
between 5 and 14.5?
• 9.75 because (5 + 14.5)/2
= 19.5/2 = 9.75
• Midpoint is the point
halfway between 2 points.

43. Midpoint
• What’s the number halfway
between 5 and 14.5?
• 9.75 because (5 + 14.5)/2
= 19.5/2 = 9.75
• Midpoint is the point
halfway between 2 points.
• The midpoint of the 2 blue
dots

44. Midpoint
• What’s the number halfway
between 5 and 14.5?
• 9.75 because (5 + 14.5)/2
= 19.5/2 = 9.75
• Midpoint is the point
halfway between 2 points.
• The midpoint of the 2 blue
dots
is the pink dot.

45. Find the Midpoint
( 3, 5 ) and ( −2, 7 )

46. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
& divide by 2.

47. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
 3 + ( −2 )  & divide by 2.
= , 
 2 

48. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
 3 + ( −2 )  & divide by 2.
= , 
 2  • Add the y-coordinates
& divide by 2.

49. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
 3 + ( −2 ) 5 + 7  & divide by 2.
= ,
 2 2   • Add the y-coordinates
& divide by 2.

50. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
 3 + ( −2 ) 5 + 7  & divide by 2.
= ,
 2 2   • Add the y-coordinates
& divide by 2.
• Simplify.

51. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
 3 + ( −2 ) 5 + 7  & divide by 2.
= ,
 2 2   • Add the y-coordinates
 1 12  & divide by 2.
= , 
2 2  • Simplify.

52. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
 3 + ( −2 ) 5 + 7  & divide by 2.
= ,
 2 2   • Add the y-coordinates
 1 12  & divide by 2.
= , 
2 2  • Simplify.
1 
=  , 6
2 

53. Find the Midpoint
( 3, 5 ) and ( −2, 7 )
• Add the x-coordinates
 3 + ( −2 ) 5 + 7  & divide by 2.
= ,
 2 2   • Add the y-coordinates
 1 12  & divide by 2.
= , 
2 2  • Simplify.
1  • Result is alway an
=  , 6 ordered pair.
2 