Q. 45.0( 1 Vote )

Each side of a sq

Answer :


Let a square be ABCD


Length of sides of square = 6


Length of diagonal = 6√2


[ For a square of side a units, diagonal equals to a√2 units]


Coordinates of centre = (–1, 2)


Distance of coordinates form centre of square


Also, diagonal AC is parallel to the line, x + y = 0


So, Equation of diagonal becomes x + y = k


As the diagonal passes through the centre of the square, coordinates of centre will satisfy the equation of diagonal.


Putting points of centre in above equation, we get


(– 1) + (2) = k


K = 1


So, equation of AC becomes, x + y = 1


x = 1 – y


Let coordinate of a point of square be (t,s)


t = 1 – s


Using distance formula between the centre and a coordinate of square,


√((1–s + 1)2 + (s–2)2 ) = 3√2


(2–s)2 + (s–2)2 = 18


2(s)2 + 8 –8s = 18


(s)2 –4s–10 = 0


S= –1 and 5


Since slope of AC = –1


slope of BD = 1


AB and CD are parallel to y–axis


And AD and BC are parallel to y axis


So, coordinates are A(2, –1), B(–4,–1),C(–4,5), D(2,5)


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