# Warm up problem: Cartesian Right Triangle 2 (harder)

**Geometry**Level 4

##### here is a link to the easier one

Given point A=(1,6) and B=(4,12) and line D=3x+7, a point C is placed on line D such that \(\triangle ABC\) is a right triangle. If the sum of all possible x-coordinates of c can be represented by\(\dfrac{p}{q}\). Find p+q.

Tip: the right angle doesn't necessarily occur at A or B.