#### Lesson 6 The Coordinate Plane

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Lesson 6 The Coordinate Plane

Coordinate Plane
y
Axes (plural of axis)
0 x-axis
0 y-axis
x
Coordinate Plane
y
Origin
x
Coordinate Plane
y
Quadrants
II
I
III
IV
x
Coordinates
Plot and label the points:
0 A(4,7)
0 B(-3,5)
0 C(4,-7)
0 D(-6,-3)
State the quadrant in which
each point is graphed.
Coordinates
State the coordinates:
0A
0B
0C
0D
0E
0F
(5,2)
(-8,-5)
(-3,5)
(4,-7)
(0,4)
(-7,0)
C
E
A
F
B
D
Distance in the coordinate plane
Kayleigh walks to a friend’s house by traveling 5 blocks
west and then 12 blocks north. She returns home later
by cutting diagonally through her neighbors’ yards.
What distance did she travel on her voyage home?
13
12
5
a 2 b2 c 2
52 122 c 2
25 144 c 2
169 c 2
169 c 2
13 c
Distance formula
0 The distance between two points x1 , y1 and x2 , y2 on
the coordinate plane (graph) can be found using the
formula:
d
x2 x1 y2 y1
2
2
http://www.bsin.k12.nm.us/schools/BHS/math/joinmath/geometry/GEO1_3.pps#257,4,Slide 4
Practice
Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth.
d=
(x2 – x1)2 + (y2 – y1)2
d=
(6 – (–2))2 + (–2 – (–6))2
d=
82 + (–8)2
d=
64 + 64 =
128
To the nearest tenth, RS = 11.3.
Midpoint Formula
In the coordinate plane, the coordinates of the midpoint
of a segment whose endpoints have coordinates ( x1 , y1 )
and ( x2 , y2 ) are x1 x2 , y1 y2 .
2
2
Example: Find the midpoint between (-2, 5) and (6, 4)
x1 y1
M=
2 6 , 5 4
2
2
M=
4 , 9 = 2, 9
2 2 2
x2 y2
Practice
AB has endpoints (8, 9) and (–6, –3). Find the coordinates of its midpoint M.
(
x1 + x2
2
8 + (–6)
2
=
=1
2
2
,
y1 + y2
2
)
9 + (–3)
6
=
=3
2
2
The coordinates of midpoint M are (1, 3).
Homework
The Coordinate Plane in
Student Practice Packet
(Page 7, #1-13)