1. Midpoint in the Coordinate Plane
Geometry
Midpoint in the Coordinate Plane

2. Entry Task
Draw 𝐴𝐵 . Construct 𝑋𝑌 such that it is a perpendicular bisector of 𝐴𝐵

3. Learning Targets Success Criteria
I understand how to use the midpoint formula to find the midpoint of any segment in the coordinate plane
Success Criteria
I can use the midpoint formula to find the midpoint formula to find the midpoint of any segment in the coordinate plane
I can use the midpoint formula to find the endpoint of any segment in the coordinate plane.
1 mins

4. The Midpoint Formula
- If A has a coordinate of -3 and B has a coordinate of 7. What is the midpoint of 𝐴𝐵 ?
If A has a coordinate of 5 and B has a coordinate of -12. What is the midpoint of 𝐴𝐵 ?
If A has a coordinate of 𝑎 and B has a coordinate of 𝑏. What is the midpoint of 𝐴𝐵 ?

5. Finding the Midpoint
𝐴𝐵 has endpoints at -4 and 9. What is the coordinate of its midpoint?
Let 𝑎=−4 and 𝑏=9.

6. Finding the midpoint
𝐸𝐹 has endpoints 𝐸(7,5) and 𝐹(2,−4). What are the coordinates of it midpoint 𝑀?

7. The Midpoint Formula In the coordinate plane:
The coordinates of the midpoint are the average of the x- coordinates and the average of the y-coordinates of the endpoints.
Given 𝐴𝐵 where A( 𝑥 1 , 𝑦 1 ) and 𝐵( 𝑥 2 , 𝑦 2 ), the coordinates of the midpoint of 𝐴𝐵 are 𝑀( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )

8. Your Turn
What is the midpoint of 𝑅𝑆 with endpoints 𝑅(5,−10) and 𝑆(3,6).
What is the midpoint of 𝑅𝑆 with endpoints 𝑅(3,−15) and 𝑆(4,7).

9. Finding the Endpoint
The midpoint of 𝐶𝐷 if 𝑀 −2,1 . One endpoints is 𝐶(−5,7). What are the coordinates of the other endpoint 𝐷.
Let 𝑀 (−2, 1) be (𝑥,𝑦) and 𝐶(−5,7) be ( 𝑥 1 , 𝑦 1 ). Let the coordinates of D be 𝑥 2 , 𝑦 2 .
−2,1 = −5+ 𝑥 2 2 , 7+ 𝑦 2 2
−2= −5+ 𝑥 2 2
−4=−5+ 𝑥 2
1= 𝑥 2
1= 7+ 𝑦 2 2
2=7+ 𝑦 2
−5= 𝑦 2
The coordinates of D are (1,-5)

10. Your TUrn
The midpoint of 𝐴𝐵 has coordinates (4,-9). Endpoint 𝐴 has coordinates (3,-5). What are the coordinates of B?

11. Learning Targets Success Criteria
I understand how to use the midpoint formula to find the midpoint of any segment in the coordinate plane
Success Criteria
I can use the midpoint formula to find the midpoint formula to find the midpoint of any segment in the coordinate plane
I can use the midpoint formula to find the endpoint of any segment in the coordinate plane.
1 mins

12. Assignment
Pg 54
#6-21 x3