Double Crosses

Geometry Level 3

The line $l_{1} : y = \dfrac{3}{2}x - 6$ is perpendicular to the line $l_{2}$ , where the $x$ -intercept of $l_{2}$ is at point $(10.5 , 0)$ .

Let point $A$ be the intersection of both lines, point $B$ be the $x$ -intercept of $l_{1}$ , point $C$ be the $y$ -intercept of $l_{2}$ , and point $O$ be the point of origin $(0 , 0)$ .