COORDINATE

PLANE

y-axis

(0,0)

Coordinate plane

We can use pythagorean theorem to find distance in the coordinate plane

Coordinate Geometry

Describe a point with an ordered pair (x, y)

Finding Distance

d is the distance of two points A(x1,y1) and B(x2,y2)

Use two points and the distance formula d = (x2 – x1)2 + (y2 – y1)2

Lets see how it works!

AB has endpoints A(1,-3) an B(-4,4). Find AB to the nearest tenth.

Label your points A( 1, -3 ) B ( -4, 4 ) x1 y1 x2 y2

Putting in calculator

Your Screen should look like this:

((-4 – 1 )2 + (4 – ( -3 ))2)

Let’s Try another:

The distance between point A (2, -1) and B (2, 5)

First label points x1 y1 x2 y2

Second put into distance formula

(2 – 2)2 + (5 – (-1))2

Punch into the calculator

Assignment

Page 46

Problems 1 – 17

FINDING

MIDPOINT

OF A

SEGMENT

A 7 B 15

To find the midpoint of a segment we get the average or mean of the two points

Simply we add the two points together and divide by 2

Example 7 + 15

2

22/2 11

11

When this line is on the coordinate plane we have to take into consideration both the x and the y coordinates

E

F

E (-2, -3)

F (2, 3 ) x1, y1 x2, y2

Formula:

x1 + x2 , y1 + y2

2 2

-2 + 2 -3 + 3

2 2

(0, 0)

TRY THIS:

Find the coordinates of the midpoint of XY with endpoints X(2, -5) and Y ( 6,13)

Label points x1, y1 x2, y2

Do we need to see this on a coordinate plane?

Use Formula x1 + x2 y1 + y2

2 2

Find the midpoint of AB

A = (0, 0)

B = (8, 4)

Finding an endpoint

The midpoint of XY has coordinates (4, -6), X has the coordinates (2, -3)

Find the Y coordinates

Let the coordinates of X be x1,y1

Use the midpoint Formula and solve for each coordinate

4 = 2 + x2

2

-6 = -3 + y2

2 endpoint Y

(6, -9)

Given the coordinate point A and the midpoint of AB has coordinates (5, -8). Find the coordinates of point B

A b

Assignment

Page 46

Problems

18 – 40 EVEN

44 & 46