Straight Lines

The orthocenter is the intersection of the altitudes. Since it is a right triangle, the altitudes meet at the vertex of the right angle. In the figure, that point is at $\left(\dfrac{-16}{13},\dfrac{15}{13}\right)$ . Using the guess and check or trial and error method, we substitute $\left(\dfrac{-16}{13},\dfrac{15}{13}\right)$ to each of the equations in the choices or options given.

Let's try $169x+26y=-178$ . We have

$169\left(\dfrac{-16}{13}\right)+26\left(\dfrac{15}{13}\right)=-178$

$-208+30=-178$

$-178=-178$ $\implies$ The statement is true so $\left(\dfrac{-16}{13},\dfrac{15}{13}\right)$ lies on the line $169x+26y=-178$ .