1. Coordinate Plane

2. Vocabulary
Coordinate Coordinate Plane Ordered Pairs Origin Plot Quadrants X-axis Y-axis

3. x y
A coordinate plane is a plane containing a horizontal number line, the x-axis, and a vertical number line, the y axis. The intersection of these axes is called the origin. 5
y-axis 4
Quadrant II 3
Quadrant I 2
x-axis 1 –5 –4 –3 –2 –1
Origin 1 2 3 4 5 –1 –2
Quadrant III –3
Quadrant IV –4 –5
The axes divide the coordinate-plane into four regions called quadrants, which are numbered I, II, III, and IV.

4. Identify the quadrant that contains each point.
Example 1
Identify the quadrant that contains each point. x y –2 2 –4 4 –1 –3 –5 5 3 1
A. Point S W
Point S lies in quadrant IV. T
B. Point T
Point T lies in quadrant I.
C. Point W S
Point W lies on the y-axis
between Quadrants I and II

5. Point N lies in quadrant II.
Practice
Identify the quadrant that contains each point. x y –2 2 –4 4 –1 –3 –5 5 3 1
A. Point N
Point N lies in quadrant II. N
B. Point X Y
Point X lies in quadrant III.
C. Point Y
Point Y lies on the origin. X

6. Finding Quadrant of a Point By Using Ordered Pairs

7. Points on a coordinate plane are identified by ordered pairs
Points on a coordinate plane are identified by ordered pairs. An ordered pair consists of two numbers in a certain order. The origin is the point (0,0). Ordered pairs are sometimes called coordinates. x y –2 2 –4 4 –1 –3 –5 5 3 1
2 units up
3 units
right
Ordered pair
(3, 2)
x-coordinate
y-coordinate
Units right
or left from 0
Units up
or down from 0

8. Plot (this means to graph) each point on a coordinate plane.
Example 2
Plot (this means to graph) each point on a
coordinate plane. x y –2 2 –4 4 –1 –3 –5 5 3 1
A. Point D (3, 3) D
Start at the origin. Move
3 units right and 3 units up.
B. Point E (–2, –3)
Start at the origin. Move
2 units left and 3 units down. E F
C. Point F (3, –5)
Start at the origin. Move
3 units right and 5 units down.

9. Start at the origin. Move 4 units right and 4 units up.
Practice
Plot each point on a
coordinate plane. x y –2 2 –4 4 –1 –3 –5 5 3 1
A. D (4, 4) E D
Start at the origin. Move
4 units right and 4 units up.
B. E (–2, 3) F
Start at the origin. Move
2 units left and 3 units up.
C. F (–1, –2)
Start at the origin. Move
1 unit left and 2 units down.

10. Give the coordinates of each point.
Example 3
Give the coordinates of each point. x y –2 2 –4 4 –1 –3 –5 5 3 1
A. Point X
(–2, 5) X
Start at the origin. Point X
is 2 units left and 5 units up. Y
B. Point Y
(–1, 0)
Start at the origin. Point Y is
one unit left on the x-axis. Z
C. Point Z
(3, –3)
Start at the origin. Point Z is 3 units right and 3
units down.

11. Start at the origin. Point L is 4 units left and 3 units up.
Practice
Give the coordinates
of each point. x y –2 2 –4 4 –1 –3 –5 5 3 1
A. Point L
(–4, 3) N L
Start at the origin. Point L
is 4 units left and 3 units up.
B. Point M
(–2, –2) M
Start at the origin. Point M is
2 units left and 2 units down.
C. Point N
(3, 4)
Start at the origin. Point N is 3 units right and 4
units up.

12. Identify the quadrant that contains each description.
Example 4
Identify the quadrant that contains each description. x y –2 2 –4 4 –1 –3 –5 5 3 1
A. Positive x-coordinate and a negative y-coordinate
Quadrant IV
B. Negative x-coordinate and a negative y-coordinate
Quadrant III.
C. X-coordinate of 0
On the y-axis

13. Give the coordinates for the following points:
star
lightning
circle
heart
cross
triangle
moon
square
diamond
music note

14. End of Today’s lesson

15. Reflections of Point on a Coordinate Plane
Two points are reflections of each other if the x-axis or y-axis forms a line of symmetry for the two points. This means that if you folded the graph along that axis, the two points would line up.

16. Reflections of Point on a Coordinate Plane
You can find the reflections of points by looking at the signs of each coordinate.

17. Reflection across the x-axis
The coordinate plane shows that point (-3, 2) and (-3, -2) are the same distance from the x-axis in opposite directions.
So, they are reflected across the x-axis.
When a point is reflected across the x axis, the x-coordinates stays the same and the y-coordinates are opposites.

18. Reflection across the y-axis
The coordinate plane shows that point (-4, 0) and (4, 0) are the same distance from the y-axis in opposite directions.
So, they are reflected across the y-axis.
When a point is reflected across the y axis, the y-coordinates stays the same and the x-coordinates are opposites.

19. Determine Reflection using Ordered Pairs
What axis are the following points reflected across?
(3,-2) and (-3, -2)
Because the y-coordinates remained the same, these points are reflected across the y-axis.
(5, 2) and (5, -2)
Because the x-coordinates remained the same, these points are reflected across the x-axis.

20. White Board Practice What axis are these points reflected across?
(2, 7) and (-2, 7)
(5, 3) and (-5, 3)
(-1, 4) and (-1, -4)
(-7, 1) and (-7, -1)
(5, -6) and (5, 6)
(-2, 4) and (-2, -4)
(8, -3) and (-8, -3)

21. Reflections of Point on a Coordinate Plane
Graph the reflection of the following points.
(4, -2) across the x
(6, 7) across the y
(-5, 3) across the y
(-6, -2) across the x
(1,6) across the y
(9, 10) across the x

22. End of today’s lesson

23. Review coordinate plane, plotting points, and reflections

24. Determine which letter is at each coordinate:
(4,9)
(-10,9)
(-4,-2)
(6,-5)
(3,5)
(6,7)
(3, -4)
(6, -4)
(6, -8)
(10,7)
Label each quadrant.
Which quadrant has (+,+) coordinates?
Which quadrant has (+,-) coordinates?
Which quadrant has (-,+) coordinates?
Which quadrant has (-,-) coordinates?

25. Graph the following points on your graph paper.
(-5, 9)
(4,3)
(-9, -9)
(1,0)
(0,4)
(2,-1)
(10, -10)
(-4, 7)
(5, 7)
(-3, 8)

26. White Board Practice What axis are these points reflected across?
(14, 9) and (-14, 9)
(8, 23) and (-8, 23)
(-16, 42) and (-16, -42)
(-29, 15) and (-29, -15)
(12, -16) and (12, 16)
(-22, 34) and (-22, -34)
(78, -93) and (-78, -93)

27. What are the coordinates of the reflected points?
(-2, 4) reflect across the y-axis
(5, -7) reflect across the x-axis
(-7, 10) reflect across the x-axis
(-5, 24) reflect across the y-axis
(92, -45) reflect across the y-axis
(62, -52) reflect across the x-axis
(-21, 41) reflect across the y-axis
(26, 92) reflect across the y-axis
(31, -12) reflect across the x-axis
(-82, -22) reflect across the y-axis