Sample quiz on equations of altitudes
Main home here.
- In a $\triangle ABC$, an altitude from vertex $A$ is $\cdots$?
- The point of intersection of the three altitudes of a triangle is known as $\cdots$?
- If a triangle contains an obtuse angle, how many of its altitudes are external (outside the triangle)?
- Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the equation of the altitude from $A$.
- Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the equation of the altitude from $B$.
- Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the equation of the altitude from $C$.
- Given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$, find the (coordinates of the) foot of the altitude from $C$.
- Find the orthocenter of $\triangle ABC$ whose vertices are located at $A(1,2),~(2,1),~C(3,3)$.
- Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the equation of the altitude from $A$.
- Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the equation of the altitude from $B$.
- Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the equation of the altitude from $C$.
- Find the orthocenter of $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$.
- Consider $\triangle ABC$ in which $\angle C=90^{\circ}$. This triangle's orthocenter is located at $\cdots$?
- Find the distance between the centroid and the foot of the altitude from $C$, given $\triangle ABC$ with vertices at $A(1,2),~B(2,1),~C(3,3)$.
- Given $\triangle ABC$ with vertices at $A(0,0),~B(1,4),~C(3,6)$, find the LENGTH of the altitude from $A$.