Unit 5: Geometric and Algebraic Connections

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Presentation transcript:

Unit 5: Geometric and Algebraic Connections 5.2 Coordinate Proofs

Pythagorean Theorem hypotenuse Distance Formula difference difference Square root difference difference

= 𝟗+𝟏 = 𝟏𝟎 = 𝟗𝟎𝟎+𝟏𝟔𝟎𝟎 =𝟓𝟎 ( −𝟐−𝟏) 𝟐 +( 𝟑−𝟒) 𝟐 = ( −𝟑) 𝟐 +(−𝟏 ) 𝟐 = ( −𝟑) 𝟐 +(−𝟏 ) 𝟐 = 𝟗+𝟏 = 𝟏𝟎 ( 𝟒𝟎−𝟏𝟎) 𝟐 +(𝟒𝟓−𝟓 ) 𝟐 = ( 𝟑𝟎) 𝟐 +(𝟒𝟎 ) 𝟐 = 𝟗𝟎𝟎+𝟏𝟔𝟎𝟎 =𝟓𝟎

Use Distance Formula to prove congruent length 𝑩𝑪 = (𝟓−𝟏 ) 𝟐 +(𝟔− 𝟑) 𝟐 = ( 𝟑) 𝟐 +(𝟒 ) 𝟐 =𝟓 𝑨𝑪 = ( 𝟏−𝟒) 𝟐 +( 𝟑−(−𝟏)) 𝟐 = ( −𝟑) 𝟐 +(𝟒 ) 𝟐 =𝟓 Use Slope Formula to prove a right triangle 𝑩𝑪 = 𝟔−𝟑 𝟓−𝟏 𝑨𝑪 = −𝟏−𝟑 𝟒−𝟏 = 𝟑 𝟒 =− 𝟒 𝟑

Use Slope Formula to prove a right triangle 𝑩𝑪 = −𝟏−𝟑 𝟐−𝟐 𝑨𝑪 = −𝟏−(−𝟏) 𝟐−(−𝟑) = −𝟒 𝟎 = 𝟎 𝟓 Undefined

𝑨𝑩 = (𝟐−𝟏 ) 𝟐 +(𝟓− 𝟐) 𝟐 = 𝟏𝟎 𝑪𝑫 = ( 𝟒−𝟓) 𝟐 +(𝟒−𝟕 ) 𝟐 = 𝟏𝟎 Use Distance Formula to prove congruent length 𝑨𝑩 = (𝟐−𝟏 ) 𝟐 +(𝟓− 𝟐) 𝟐 = 𝟏𝟎 𝑪𝑫 = ( 𝟒−𝟓) 𝟐 +(𝟒−𝟕 ) 𝟐 = 𝟏𝟎 𝑩𝑪 = (𝟓−𝟐 ) 𝟐 +(𝟕−𝟓 ) 𝟐 = 𝟏𝟑 𝑨𝑫 = ( 𝟒−𝟏) 𝟐 +( 𝟒−𝟐) 𝟐 = 𝟏𝟑

𝑨𝑩 = (−𝟐−(−𝟑) ) 𝟐 +(𝟔− 𝟐) 𝟐 = 𝟏𝟕 𝑪𝑫 = ( 𝟏−𝟐) 𝟐 +(𝟑−𝟕 ) 𝟐 = 𝟏𝟕 𝑩𝑪 = (𝟐−(−𝟐) ) 𝟐 +(𝟕−𝟔 ) 𝟐 = 𝟏𝟕 𝑨𝑫 = ( 𝟏−(−𝟑)) 𝟐 +( 𝟑−𝟐) 𝟐 = 𝟏𝟕

𝑨𝑩 = 𝟐−𝟎 𝟑−(−𝟑) 𝑨𝑫 = −𝟑−𝟎 −𝟐−(−𝟑) 𝑨𝑩 = (𝟑−(−𝟑) ) 𝟐 +(𝟐−𝟎 ) 𝟐 Use Slope Formula to prove a right triangle 𝑨𝑩 = 𝟐−𝟎 𝟑−(−𝟑) = 𝟏 𝟑 𝑨𝑫 = −𝟑−𝟎 −𝟐−(−𝟑) =−𝟑 Use Distance Formula to prove congruent length 𝑨𝑩 = (𝟑−(−𝟑) ) 𝟐 +(𝟐−𝟎 ) 𝟐 = ( 𝟔) 𝟐 +(𝟐 ) 𝟐 = 𝟒𝟎 𝑪𝑫 = (−𝟐−𝟒 ) 𝟐 +(−𝟑−(−𝟏) ) 𝟐 = ( −𝟔) 𝟐 +(−𝟐 ) 𝟐 = 𝟒𝟎

𝑨𝑩 = 𝟒−𝟎 𝟎−(−𝟑) 𝑨𝑫 = −𝟑−𝟎 −𝟏−(−𝟑) 𝑨𝑩 = (𝟎−(−𝟑) ) 𝟐 +(𝟒−𝟎 ) 𝟐 Use Slope Formula to prove a right triangle 𝑨𝑩 = 𝟒−𝟎 𝟎−(−𝟑) = 𝟒 𝟑 𝑨𝑫 = −𝟑−𝟎 −𝟏−(−𝟑) =− 𝟑 𝟒 Use Distance Formula to prove congruent length 𝑨𝑩 = (𝟎−(−𝟑) ) 𝟐 +(𝟒−𝟎 ) 𝟐 = ( 𝟑) 𝟐 +(𝟒 ) 𝟐 =𝟓 𝑩𝑪 = (𝟒−𝟎 ) 𝟐 +(𝟏−𝟒 ) 𝟐 = ( 𝟒) 𝟐 +(−𝟑 ) 𝟐 =𝟓