# Brilli's faithfulness for Billi

Geometry Level 4

Brilli the ant had his ant hill named $$B_1$$ which had coordinates $$(8,10)$$.Brilli had his girlfriend named Billi who had her ant hill named $$B_2$$ which had coordinates $$(-2,30)$$. Once Billi was thirsty and she called Brilli to get her some water from a river named Bribill which had equation $$2x+y-6=0$$. Thus to not to displease his girlfriend , Brilli had to take the quickest path which will lead him to Bribill river first and then to Billi's ant hill. Brilli calculated a point $$P$$ on the Bribill river such that if he starts from his ant hill , goes to point $$P$$ and then goes to Billi's ant hill , he would have taken the shortest possible path requiring less efforts and time.

Find the sum of the coordinates of point $$P$$ that Brilli calculated.

Details and Assumptions:

• Assume the ant-hills as points and the river as a "straight" line.

• Brilli was always perfect in his calculations.

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