Chapter 6.6, Problem 66HP

To determine

To calculate:

The equation of line contained by the mid-segment

Answer to Problem 66HP

The equation of line contained by the mid-segment is $\mathrm{y}=\mathrm{x}-2$

Explanation of Solution

Given information:

  $\begin{array}{l}\mathrm{y}=\mathrm{x}+4\\ \mathrm{y}=\mathrm{x}-8\end{array}$

Calculation:

First draw both lines $\left(\mathrm{y}=\mathrm{x}+4\right)$ and $\left(\mathrm{y}=\mathrm{x}-8\right)$

in the coordinate plane as:

  

The mid-segment of trapezoid is parallel to each base according to the Trapezoid mid-segment theorem.

Know that:

The value of the mid-segment of trapezoid is one half of the sum of the lengths of bases. Therefore, the slope of line containing the mid-segment is $1$ .

The $\mathrm{y}-$ intercepts of the bases is $\frac{4+\left(-8\right)}{2}=-2$ .

Therefore, the equation of line containing the mid-segment is $\mathrm{y}=\mathrm{x}-2$ .