COORDINATE PLANE

Coordinate plane Quadrant I (+, +) Quadrant II (-, +) y-axis origin x-axis (0,0) Quadrant III (-, -) Quadrant IV (+, -)

Coordinate Geometry Describe a point with an ordered pair (x, y) Finding Distance Use two points and the distance formula d = (x2 – x1)2 + (y2 – y1)2 d is the distance of two points A(x1,y1) and B(x2,y2)

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 (-4 -1)2 +( 4 – (-3))2 -52 + 72 25 + 49 74 8.6

Let’s put this in the calculator: Punch in: ( -4 - 1 ) 2 + ( 4 - -3 ) 2

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 6

Assignment Page46 Problems 1 – 17

FINDING MIDPOINT OF A SEGMENT

A 7 B 15 11 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

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 ) x1, y1 x2, y2 Formula: x1 + x2 , y1 + y2 2 2 -2 + 2 -3 + 3 2 2 (0, 0) F E

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 2 + 6 -5 + 13 2 2 (4, 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 -12 = -3 + y2 -9 = y2 endpoint Y (6, -9) 8 = 2 + x2 6 = x2

Assignment Page 46 Problems 18 – 31 32 – 40 for midpoint only 44- 46