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Inside the square is of length 6 units and the centre of the square is (-1,2) one of its diagonal is parallel to X + Y =0 find the coordinates of the vertices of the square

Inside the square is of length 6 units and the centre of the square is (-1,2) one of its diagonal is parallel to X + Y =0 find the coordinates of the vertices of the square

Grade:11

1 Answers

Soumya Ranjan Mohanty
117 Points
6 years ago
Dear student,
center of square ABCD =O(-1,2)
given:AB=BC=CD=DA=6 units
so AC= 6*sqrt2 units so AO=AC/2 =3*sqrt2
eqn of AC is x+y=k (as parallel to x+y=0)
O lies on AC:
(-1,2)=>-1+2=k =>k=1
therefore eqn of AC: x+y=1
let A be (a,1-a)
O is midpoint of AC
so AO^2=(a+1)^2+(-a-1)^2= (3*sqrt2)^2
=>a=2 or -4
as AC has slope =-1, so AB and CD are parallel to x axis whereas AD and BC are parallel to y axis
therefore we get A = (2, -1) ,  B(2-6, -1) =B(-4,-1), C(-4, 5) and D = (2, -1 + 6) = D= (2, 5) [Answer]
Hope this helps.
Soumya Ranjan Mohanty.

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