Question

in triangle abc, points d and e are the mid - points of $overline{ab}$ and $overline{ac}$ respectively. what are the slope and length of $overline{de}$, if the slope and length of $overline{bc}$ are 0.5 and 3.2 units, respectively?
a. slope = 0.25, length = 1.6 units
b. slope = - 2, length = 3.2 units
c. slope = 0.5, length = 1.6 units
d. slope = 0.25, length = 3.2 units
e. slope = - 2, length = 1.6 units

Explanation:

Step1: Recall the mid - point theorem property for slope

In a triangle, if a line segment joins the mid - points of two sides of a triangle, it is parallel to the third side. Parallel lines have the same slope. Since $D$ and $E$ are mid - points of $\overline{AB}$ and $\overline{AC}$ respectively, $\overline{DE}\parallel\overline{BC}$. Given the slope of $\overline{BC}$ is $0.5$, the slope of $\overline{DE}$ is also $0.5$.

Step2: Recall the mid - point theorem property for length

The length of the line segment joining the mid - points of two sides of a triangle is half the length of the third side. Given the length of $\overline{BC}$ is $3.2$ units. Let the length of $\overline{DE}$ be $l$. Then $l=\frac{1}{2}\times$ length of $\overline{BC}$. So $l = \frac{1}{2}\times3.2=1.6$ units.

Answer:

C. slope = 0.5, length = 1.6 units