Let ABCD be a square two of whose adjacent vertices, say A, B on the positive X-axis and the positive Y-axis, respectively. If C has co-coordinates (u,v) in the first quadrant, determine the area of ABCD in terms of u and v.

Explanation

`AB=sqrt(a^2+b^2`

`m_(AD)=-b/a`

`m_(BC)=a/b= tantheta`

`sintheta=a/sqrt(a^2+b^2),costheta=b/sqrt(a^@+b^2`

`(x-0)/costheta=(y-b)/sintheta=sqrt(a^2+b^2`

`U=b,V-b=a`

`V=a+b`

`a=(V-U)`

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