Question

In the given figure, AC is the diagonal of the square ABCD. The

coordinates of the other two points are B( _____, ______ ) and

D( ______, ______ ).
​

Answer 1

Given : AC is the diagonal of the square ABCD.  A = ( 0 , 4)  , C = ( 4 , 0)

To Find :  The  coordinates of the other two points are B( _____, ______ ) and  D( ______, ______ ).​

Solution:

A = ( 0 , 4)  , C = ( 4 , 0)

Let say  B is ( x , y)

As lines of square are perpendicular

Then  ( y - 4)/(x - 0)  *  ( y - 0)/(x - 4)  = - 1

=> (y - 4)/x  *  y /(x - 4)  = - 1

=>  y² - 4y  =  -x² + 4x

=> x² + y²  = 4x + 4y

Length of AC = √(4 - 0)² + (0 - 4)² = 4√2

Side of square = diagonal / √2  = 4√2 /√2  = 4

x²  + (y - 4)² = 4² => x²  + y² - 8y  + 16 = 16  => x²  + y² = 8y

(x - 4)² + y² = 4² => x² - 8x  + 16  + y²  = 16  => x²  + y² = 8x

8x = 8y

=> x = y

x² + x² = 8x

=> 2x² - 8x = 0

=> x² - 4x  = 0

=> x(x - 4)= 0

=> x = 0 , 4

Points are ( 0 , 0)  & ( 4 , 4)

coordinates of the other two points are B( ___0__, __0___ ) and

D( ___4__, __4___ ).​  

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