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)=(-3-6)/(-2-3)=(9)/(5) \\ \\ m_(AC)=(-3-5)/(-2-(-5))=-(8)/(3) \\ \\ m_(BC)=(5-6)/(-5-3)=(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))=-(5)/(9) \\ \\ m_(A(AC))=(3)/(8) \\ \\ m_(A(BC))=-8 \end{gathered}`