The Coordinate Plane Mrs. King Geometry Unit 1, Lesson 6.

The Coordinate Plane

Mrs. KingGeometry

Unit 1, Lesson 6

Coordinate Plane

Axes (plural of axis)0 x-axis0 y-axis

x

y

Coordinate Plane

Origin

x

y

Coordinate Plane

Quadrants

x

y

III

III IV

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:0 A0 B0 C0 D0 E0 F

A

B

C

D

E

F

(5,2)(-8,-5)

(-3,5)(4,-7)(0,4)(-7,0)

Distance in the coordinate planeKayleigh 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?

5

1213

222 cba 222 125 c214425 c2169 c

2169 cc13

Distance formula

0The distance between two points and on the coordinate plane (graph) can be found

using the formula:

212

212 yyxxd

11, yx 22 , yx

http://www.bsin.k12.nm.us/schools/BHS/math/joinmath/geometry/GEO1_3.pps#257,4,Slide 4

d = 82 + (–8)2

Find the distance between R(–2, –6) and S(6, –2) to the nearest tenth.

To the nearest tenth, RS = 11.3.

d = (x2 – x1)2 + (y2 – y1)2

d = (6 – (–2))2 + (–2 – (–6))2

d = 64 + 64 = 128

Practice

Midpoint Formula

1 2 1 2,2 2

x x y y

1 1( , )x y

42

,92

= 2,

92

M =

2 62

,5 4

2

M =

Find the midpoint between (-2, 5) and (6, 4) Example:

In the coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and are .2 2( , )x y

x1 y1 x2 y2

The coordinates of midpoint M are (1, 3).

AB has endpoints (8, 9) and (–6, –3). Find the coordinates of its midpoint M.

( , )x1 + x2

2

y1 + y2

2

8 + (–6)2 = = 1

22

9 + (–3)2 = = 3

62

Practice

Homework

The Coordinate Plane in Student Practice Packet(Page 7, #1-13)