Midpoint in the Coordinate Plane

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Presentation transcript:

Midpoint in the Coordinate Plane Geometry Midpoint in the Coordinate Plane

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

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

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 ?

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

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

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 )

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).

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)

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

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

Assignment Pg 54 #6-21 x3