COORDINATE PLANE

Coordinate plane y-axis (0,0)

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(x 1 ,y 1 ) and B(x 2 ,y 2 )

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 ) x 1 y 1 x 2 y 2

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 x Second put into distance formula (2 – 2) 2 + (5 – (-1)) 2 1 y 1 x 2 y 2 Punch into the calculator

Assignment Page 46 Problems 1 – 17

FINDING MIDPOINT OF A SEGMENT

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 22/2 11 2

When this line is on the coordinate plane we have to take into consideration both the x and the y coordinates E (-2, -3) F (2, 3 ) x 1 , y 1 x 2 , y 2 F Formula: x 1 + x 2 , y 1 + y 2 2 2 E -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 x 1 , y 1 x 2 , y 2 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 x 1 ,y 1 Use the midpoint Formula and solve for each coordinate 4 = 2 + x 2 2 -6 = -3 + y 2 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