Chapter 13.4, Problem 12MRE

a.

To determine

To Find: The slope of altitude from B to $\overrightarrow{AC}$ .

Answer to Problem 12MRE

slope of altitude from B $=\frac{2}{3}$ .

Explanation of Solution

Given information: Triangle ABC has vertices $A\left(6,0\right),B\left(4,8\right),C\left(2,6\right)$ .

Formula used: Two given points $A\left(x_1,y_1\right)$ and $B\left(x_2,y_2\right)$

Slope $=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

slope of altitude from B $=\frac{-1}{\text{Slope of }AC}$ .

  $\begin{array}{l}\text{Slope of }AC=\frac{6-0}{2-6}\\ \text{Slope of }AC=\frac{-3}{2}\end{array}$

slope of altitude from B $=\frac{2}{3}$ .

b.

To determine

To Find: The slope of perpendicular bisector of $\overrightarrow{AB}$ .

Answer to Problem 12MRE

The slope of perpendicular bisector of $\overrightarrow{AB}$ $=\frac{1}{4}$ .

Explanation of Solution

Given information: Triangle ABC has vertices $A\left(6,0\right),B\left(4,8\right),C\left(2,6\right)$ .

Formula used: Two given points $A\left(x_1,y_1\right)$ and $B\left(x_2,y_2\right)$

Slope $=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

The slope of perpendicular bisector of $\overrightarrow{AB}$ $=\frac{-1}{\text{Slope of }AB}$ .

  $\begin{array}{l}\text{Slope of }AB=\frac{8-0}{4-6}\\ \text{Slope of }AB=-4\end{array}$

The slope of perpendicular bisector of $\overrightarrow{AB}$ $=\frac{1}{4}$ .