1. 1.6: The Coordinate Plane Objective:
To find the distance between 2 points in the coordinate plane
To find the coordinates of a midpoint of a segment on the coordinate plane

2. (-, +) ( +, +) a.) (5, 2) b.) (-2, -4) c.) (5, -2) d.) (-4, 5) (-, -)
IN COORDINATE GEOMETRY, WE CALL A POINT AN ORDERED PAIR: (x, y) (these are the coordinates of the point)
(-, +)
( +, +)
Graph the following points:
a.) (5, 2)
b.) (-2, -4)
c.) (5, -2)
d.) (-4, 5)
(-, -)
( +, -)

3. The Distance Formula
Used to find the distance between two points: A( x1, y1) and B(x2, y2)
You also could just plot the points and use the Pythagorean Theorem!!

4. Find the distance between the two points
Find the distance between the two points. Round your answer to the nearest tenth.
T(5, 2) and R(-4, -1)
Take a look at example 2, p. 44
2. A( -2, -3) and B(1, 3)

5. When would you need to use the distance formula on the coordinate plane?
Can you always use the Pythagorean Theorem instead?

6. Plot these points and find the length of a diagonal of the rectangle.
A(2, 1); B(2, -5); C(-4, -5); D(-4, 1)

7. Midpoint Formula Find the midpoint coordinates between 2 points
Find by averaging the x-coordinates and the y-coordinates of the endpoints
(x2, y2)
(x1, y1)

8. Find the coordinates of the midpoint of
Q(3, 5) and S(7, -9)
Q( -4, 4) and S(5, -1)

9. Finding an Endpoint Using the Midpoint Formula
The midpoint of is M(3. 4). One endpoint is A (-3, -2). Find the coordinates of the other endpoint, B. x- coordinate: y-coordinate:
Double the midpoint coordinate then subtract the endpoint

10. Find the other endpoint: Endpoint: (2, 5) Midpoint: (5, 1)

11. Warm-up 1. Find the distance between ( 10, -2 ) and (-8, 6 ).
2. Find the midpoint of segment AB if A is at ( -4, 12 ) and B is at ( 10, -6 ).
3. If one endpoint of a segment is at (6, -10) and the midpoint is at ( 2, 4 ) find the other endpoint of the segment.

12. A surveyor locates a water well at ( 2, -3 )
A surveyor locates a water well at ( 2, -3 ). The farmer needs to pipe this water to a cattle pond at ( 10, 11 ). Find the length of the pipe the farmer must buy.