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Complete the coordinate proof of the theorem.

Given:  ABCD is a square.

Prove: The diagonals of ​ ABCD ​ are perpendicular.

 

 

Enter your answers in the boxes.

 

The coordinates of  square ABCD are A(0, 0) , B(________, 0), C(_____, a), and ​ D(0,  a) .

 

The slope of AC¯¯¯¯¯ , when simplified, is equal to_________ .

 

The slope of BD¯¯¯¯¯, when simplified, is equal to −1 .

 

The product of the slopes is equal to ____________.

 

Therefore, the diagonals of ​ ABCD ​ are perpendicular.

 Jan 7, 2018

Best Answer 

 #1
avatar+8437 
+1

The coordinates of square ABCD are  A(0, 0) ,  B(a, 0) ,  C(a a) , and ​ D(0,  a) .

 

The slope of  AC   =   [a - 0] / [a - 0]   =   1 .

 

The slope of  BD   =   -1 .

 

The product of the slopes   =   1 * -1   =   -1 .

 Jan 7, 2018
 #1
avatar+8437 
+1
Best Answer

The coordinates of square ABCD are  A(0, 0) ,  B(a, 0) ,  C(a a) , and ​ D(0,  a) .

 

The slope of  AC   =   [a - 0] / [a - 0]   =   1 .

 

The slope of  BD   =   -1 .

 

The product of the slopes   =   1 * -1   =   -1 .

hectictar Jan 7, 2018

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