A rectangle ABCD is inscribed in a circle with a diameter lying along the line $3\mathrm{y}=\mathrm{x}+10.$ If $\mathrm{A}=(-6,7),\mathrm{B}=(4,7)$ then area of the rectangle is

Perpendicular bisector of (-6,7) and (4,7) is x= -1

Centre lies on 3y = x + 10, and x= -1

$\Rightarrow 3\mathrm{y}=9\Rightarrow \mathrm{y}=3$

Centre (-1,3) $\Rightarrow D(4,-1)$

AB=10,BD=8

Area = 10 x 8