In the given figure, AC is the diagonal of the square ABCD. The coordinates of the other two points are B( _____, ______ ) and D( ______, ______ ).
Answers
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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