Question

. 3. Find the slope of the altitude on each side of triangle ABC. (d) A(-2,-3), B(3,6). C(-5,5)

Answer 1

An altitude in a triangle is a segment that goes from a vertex to the opposite side and it's perpendicular to it.

Knowing the vertices of the triangle ABC, you can draw the triangle on a Coordinate plane:

Now find the slope of each side using this formula:

$m=\frac{y_2-y_1}{x_2-x_1_{}}$

Then, you get:

$\begin{gathered} m_{AB}=\frac{-3-6}{-2-3}=\frac{9}{5} \\ \\ m_{AC}=\frac{-3-5}{-2-(-5)}=-\frac{8}{3} \\ \\ m_{BC}=\frac{5-6}{-5-3}=\frac{1}{8}_{} \end{gathered}$

By definition, the slopes of perpendicular lines are opposite reciprocals. Knowing this, you can determine that the slopes of the altitudes on each side of triangle ABC are:

$\begin{gathered} m_{A(AB)}=-\frac{5}{9} \\ \\ m_{A(AC)}=\frac{3}{8} \\ \\ m_{A(BC)}=-8 \end{gathered}$