1. COORDINATE
PLANE

2. Coordinate plane
y-axis
(0,0)

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

4. 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)

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

6. 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

7. Putting in calculator
Your Screen should look like this:
((-4 – 1 )2 + (4 – ( -3 ))2)

8. Let’s Try another:
The distance between point A (2, -1) and B (2, 5)
First label points x1 y x2 y2
Second put into distance formula
(2 – 2)2 + (5 – (-1))2
Punch into the calculator

9. Assignment
Page 46
Problems 1 – 17

10. FINDING
MIDPOINT
OF A
SEGMENT

11. A 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 2
22/2 11

12. 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, y x2, y2
Formula:
x1 + x2 , y1 + y2
(0, 0) F E

13. TRY THIS:
Find the coordinates of the midpoint of XY with endpoints X(2, -5) and Y ( 6,13)
Label points x1, y x2, y2
Do we need to see this on a coordinate plane?
Use Formula x1 + x y1 + y2

14. Find the midpoint of AB
A = (0, 0)
B = (8, 4)

15. 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 = x2 2
-6 = -3 + y2 2
endpoint Y
(6, -9)

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

17. Assignment
Page 46
Problems
18 – 40 EVEN
44 & 46