Question

in triangle abc, points d and e are the midpoints 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 = -2, length = 3.2 units\
b. slope = 0.25, length = 1.6 units\
c. slope = 0.5, length = 1.6 units\
d. slope = -2, length = 1.6 units\
e. slope = 0.25, length = 3.2 units

Explanation:

Step1: Apply Midsegment Slope Property

Midsegment $\overline{DE} \parallel \overline{BC}$, so slope of $\overline{DE}$ = slope of $\overline{BC} = 0.5$

Step2: Apply Midsegment Length Property

Length of midsegment $\overline{DE} = \frac{1}{2} \times$ length of $\overline{BC}$
$\text{Length of } \overline{DE} = \frac{1}{2} \times 3.2 = 1.6$ units

Answer:

C. slope = 0.5, length = 1.6 units