1. 1.8 The Coordinate Plane

2. You will learn to name and graph ordered pairs on a coordinate plane.
What You'll Learn
You will learn to name and graph ordered pairs on a coordinate plane. y x 5 -4 -2 1 3 -5 -1 4 -3 2
In coordinate geometry, grid paper is used to locate points.

3. You will learn to find the distance of a line segment.
What You'll Learn
You will learn to find the distance of a line segment. B A
The distance of a line segment AB
is found by the formula

4. You will learn to find the coordinates of the midpoint of a segment.
What You'll Learn
You will learn to find the coordinates of the midpoint of a segment. B A C
The midpoint of a line segment AB
is the point C that ______
the segment.
bisects

5. The horizontal number line is called the ______. x-axis
Lets’ look
at the
grid. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Quadrant II
(–, +)
Quadrant I
(+, +) O
Quadrant III
(–, –)
Quadrant IV
(+, –)
The horizontal number line is called the ______.
x-axis
The vertical number line is called the ______.
y-axis

6. The point of intersection of the two axes is called the _____. origin
Lets’ look
at the
grid. y x 5 -4 -2 1 3 -5 -1 4 -3 2
Quadrant II
(–, +)
Quadrant I
(+, +) O
Quadrant III
(–, –)
Quadrant IV
(+, –)
The point of intersection of the two axes is called the _____.
origin
The two axes separate the plane into four regions called _________.
quadrants

7. Now, see if you can name the points. B B A A C C D D Point A(x, y) =5 -4 -2 1 3 -5 -1 4 -3 2
(–3, 2) B B A
(3, 2) A C
(–3, –2) C D
(3, –2) D
Point A(x, y) =
(3, 2)
Point C(x, y) =
(–3, –2)
Point B(x, y) =
(–3, 2)
Point D(x, y) =
(3, –2)

8. OK, It’s
your turn
On a piece of grid paper draw lines representing the x-axis and the y-axis.
Graph :
A(2, 4) y x 5 -4 -2 1 3 -5 -1 4 -3 2
B(2, 0) A
C(2, –3)
D(2, –5) B C D

9. What do you notice about the graphs of these points?
OK, It’s
your turn
Consider these questions:
What do you notice about the graphs of these points?
x = 2
They lie on a vertical line. y x 5 -4 -2 1 3 -5 -1 4 -3 2 A B C D

10. What do you notice about the x-coordinates of these points?
OK, It’s
your turn
Consider these questions:
What do you notice about the x-coordinates of these points?
A(2, 4) y x 5 -4 -2 1 3 -5 -1 4 -3 2
B(2, 0) A
C(2, –3)
D(2, –5) B
They are the same number. C D

11. OK, It’s
your turn
Consider these questions:
Write a general statement about ordered pairs that have the same x-coordinate.
They lie on a vertical line that intersects the x-axis at the x-coordinate. y x 5 -4 -2 1 3 -5 -1 4 -3 2 A B C D

12. Find the distance between two points.
How about the
distance between
two points
Find the distance between two points.
(-2,5) and (8,3) d=

13. Find the midpoint between two points.
Lets’ look at
finding a midpoint.
Find the midpoint between two points.
(0.45,7) and (-0.3,-9)
(0.075,-1)

14. Find the midpoint, C(x, y), of a segment on the coordinate plane.y x 10 -1 2 4 6 8 -2 3 7 1 5 9
x = 1
x = 9
A(1, 7)
B(9, 3)
y = 7
C(5, 5) y x
y = 3

15. Graph A(1, 1) and B(7, 9) Draw AB Find the midpoint of AB. B(7, 9) Cy x 10 -1 2 4 6 8 -2 3 7 1 5 9
B(7, 9)
Find the midpoint of AB. C
C(4, 5)
A(1, 1)

16. Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B.
x-coordinate of B
y-coordinate of B
B(-1, 8)
Replace x1 with 7 and y1 with 2
B(x, y) is somewhere over there.
C(3, 5)
midpoint
A(7, 2)
Multiply each
side by 2
Add or subtract to isolate the variable

17. In the figure, B is the midpoint of AC.
Find the value of x.
5x - 6 2x C B A
Check!
Since B is the midpoint:
AB = BC
AB = 5x – 6
= 5(2) – 6
= 10 – 6
= 4
Write the equation involving x:
5x – 6 = 2x
Solve for x:
5x – 2x – 6 = 2x – 2x
3x – = 0 + 6
3x = 6
x = 2
BC = 2x
= 2(2)
= 4

18. Assignment

19. 1.8 The Coordinate Plan A B Geometryy x 5 -1 2 4 -2 1 -3 3
1. Name the coordinates of each point. A
2. Graph point C at (0, –4).
3. Graph x = –4. B
4. Graph y = 2.
5. Graph and label the intersection of x = – and y = 2
6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ?
7. In the figure below, R is the midpoint of QS. Find the value of d.
8. True or False: If AB  CD, then CD  AB.
9. True or False: If AB  BC, then B is the midpoint of AC.
d + 4 3d S R Q
10. Find the distance: (-4,9),(1,-3)
11. Find the midpoint: (9,-2),(12,-14)

20. 1.8 The Coordinate Plan A B Geometryy x 5 -1 2 4 -2 1 -3 3
1. Name the coordinates of each point.
A = (2, 0)
B = (3, –2) A
2. Graph point C at (0, –4).
3. Graph x = –4. B
4. Graph y = 2.
5. Graph and label the intersection of x = – and y = 2
6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ?
7. In the figure below, R is the midpoint of QS. Find the value of d.
8. True or False: If AB  CD, then CD  AB.
9. True or False: If AB  BC, then B is the midpoint of AC.
d + 4 3d S R Q
10. Find the distance: (-4,9),(1,-3)
11. Find the midpoint: (9,-2),(12,-14)