Question 14
Consider the points $A(0, 12),$ $B(10, 9),$ $C(8, 0),$ and $D(-4, 7).$ There is a unique square $\mathcal{S}$ such that each of the four points is on a different side of $\mathcal{S}.$ Let $K$ be the area of $\mathcal{S}.$ Find the remainder when $10K$ is divided by $1000.$