The Problem is:

"A horseman left the village A at point $\displaystyle (1,4)$ and began riding along a straight road whose direction was given by the vector v=7i+4j. The at some point he turned at a right angle; He never changed direction again until he arrived in the village $\displaystyle B$ at the point with the coordinates (8,13). At the point where he made the turn he buried a jar full of silver coins, Unfortunately, he forgot the coordinates of the point. Find the point.

So I drew the graph and labeled the point where he changed direction as $\displaystyle C$ with the coordinates $\displaystyle (x,y)$. This means the vector $\displaystyle CA$ is <x-1, y-4> and the vector $\displaystyle BC$ is <8-x,13-y>.

Next, I worked out the dot product of the two vectors to be (x-1)(8-x)+(y-4)(13-y)=0 It has to be equal to 0 since the angle is a right angle and it is orthogonal. Been working on this problem for about 45 minutes, and have no idea how to solve it. Any help is appreciated.