1. Connecting Algebra
with the
Coordinate Plane

2. First, let’s take a look at….

3. A little history

4. A little history René Descartes (1596-1650) philosopher mathematician
joined algebra and geometry
credited with---
Cartesian plane

5. The year is Lying on his back, French mathematician René Descartes, watches a fly crawl across the ceiling. Suddenly, an idea comes to him. He visualizes two number lines, intersecting at a 90° angle. He realizes that he can graph the fly's location on a piece of paper. Descartes called the main horizontal line the x-axis and the main vertical line the y-axis. He named the point where they intersect the origin.

6. Descartes represented the fly's location as an ordered pair of numbers.
The first number, the x-value, is the horizontal distance along the x-axis, measured from the origin.
The second number, the y-value, is the vertical distance along the y-axis, also measured from the origin.

7. Now, let’s take a look at…

8. Cartesian plane Formed by intersecting two real number lines at
right angles

9. Cartesian plane
Horizontal axis is
usually called the
x-axis

10. Cartesian plane
Vertical
axis is
usually called the
y-axis

11. Cartesian plane
Also called:
x-y plane
rectangular
coordinate
system

12. Cartesian plane II I
Divides into
Four Quadrants
and…
III IV

13. of the two axes is called the origin
Cartesian plane
The intersection
of the two axes is called the origin

14. The quadrants do not include the axes
Cartesian plane II I
Math Alert
The quadrants do not include the axes
III IV

15. A point on the x or y axis is not in a quadrant
Cartesian plane II I
Math Alert
A point on the x or y axis is not in a quadrant
III IV

16. x-y plane is associated with an ordered pair, (x,y)
Cartesian plane
Each point in the
x-y plane is associated with an ordered pair, (x,y)
(x,y)
(x,y)
(x,y)
(x,y)

17. Cartesian plane The x and y of the ordered pair,
(x,y), are called its coordinates
(x,y)
(x,y)
(x,y)
(x,y)

18. There is an infinite amount of points in the Cartesian plane
Math Alert
There is an infinite amount of points in the Cartesian plane

19. The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers.
COORDINATE PLANE
The point (0, 0) on a coordinate plane, where the x-axis and the y-axis intersect.
ORIGIN

20. Take note of these graphing basics

21. Cartesian plane Always start at (0,0)---every
point “originates” at the origin

22. ---remember the directions of both the x and y
Cartesian plane y
In plotting (x,y)
---remember the directions of both the x and y
axis x

23. Cartesian plane
(x,---)
x-axis goes
left and right

24. Cartesian plane
(---,y)
y-axis goes
up and down

25. Now, let’s look at graphing…

26. Cartesian plane
Start at (0,0)
( , ---)
Move right 2 +

27. Cartesian plane
(---, )
(---, 1)
Move up 1 +

28. Now, let’s look at graphing…

29. Cartesian plane
Start at (0,0)
( , ---)
Move right 4 +

30. Cartesian plane
(---, )
(---, -2)
Move down 2 -

31. Cartesian plane
Start at (0,0)
( , ---)
Move left 3 -

32. Cartesian plane +
(---, )
(---, 5)
Move up 5

33. Cartesian plane
Start at (0,0)
(none,---)
No move right or left

34. Cartesian plane +
(0, )
(---, 4)
Move up 4

35. Now, let’s look at graphing…

36. Cartesian plane
Start at (0,0)
( ,---)
Move left 5

37. Cartesian plane
( ---, 0)
No move up
or down

38. Points in Quadrant 2 have negative x but positive y coordinates.
Points in Quadrant 1 have positive x and positive y coordinates.
To make it easy to talk about where on the coordinate plane a point is, we divide the coordinate plane into four sections called quadrants.
Points in Quadrant 3 have negative x and negative y coordinates.
Points in Quadrant 4 have positive x but negative y coordinates.

40. Cartesian plane Approximate the coordinates of the point---
Directions:
Approximate
the coordinates
of the point---
Or what is the
‘(x,y)’of the
point?

41. Cartesian plane
Directions:
Approximate
the coordinates
of the point

42. Cartesian plane
Directions:
Approximate
the coordinates
of the point

43. Cartesian plane
Directions:
Approximate
the coordinates
of the point

44. Cartesian plane
Directions:
Approximate
the coordinates
of the point

45. Cartesian plane
Directions:
Approximate
the coordinates
of the point

46. Cartesian plane
Directions:
Approximate
the coordinates
of the point

47. Cartesian plane
Directions:
Approximate
the coordinates
of the point

48. Cartesian plane
Directions:
Approximate
the coordinates
of the point

49. Cartesian plane
Directions:
Approximate
the coordinates
of the point

50. Cartesian plane
Directions:
Approximate
the coordinates
of the point

51. Cartesian plane
Directions:
Approximate
the coordinates
of the point

52. Cartesian plane Find the coordinates of the point two units
Directions:
Find the
coordinates of
the point two units
to the left of the
y-axis and five
units above the
x-axis

53. Cartesian plane Find the coordinates of the point two units
Directions:
Find the
coordinates of
the point two units
to the left of the
y-axis and five
units above the
x-axis

54. the point on the x-axis and three units to the left of the
Cartesian plane
Directions:
Find the
coordinates of
the point on the x-axis and three units to the left of the
y-axis

55. a point on the x-axis and three units to the left of the
Cartesian plane
Directions:
Find the
coordinates of
a point on the x-axis and three units to the left of the
y-axis

56. You can do this!