Question

Find H and verify that it lies on all three altitudes.

$$\begin{gathered}A=(49,-16),\quad B=(37,8)\ C=(1,8)\end{gathered}$$

Accepted Answer

$$\begin{gathered}H=(49,32)\ (H-A)\cdot(C-B)=0\ (H-B)\cdot(A-C)=0\ (H-C)\cdot(B-A)=0\end{gathered}$$

Answer

$$\begin{gathered}H=(48,31)\ (H-A)\cdot(C-B)=0\ (H-B)\cdot(A-C)=0\ (H-C)\cdot(B-A)=0\end{gathered}$$

Answer

$$\begin{gathered}H=(49,33)\ (H-A)\cdot(C-B)=0\ (H-B)\cdot(A-C)=0\ (H-C)\cdot(B-A)=1\end{gathered}$$

Answer

$$\begin{gathered}H=(50,32)\ (H-A)\cdot(C-B)=0\ (H-B)\cdot(A-C)=0\ (H-C)\cdot(B-A)=0\end{gathered}$$

Practice: Triangle Orthocenter - Prove Altitude Concurrency