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 = 0.25, length = 3.2 units
b. slope = -2, length = 1.6 units
c. slope = 0.25, length = 1.6 units
d. slope = 0.5, length = 1.6 units
e. slope = -2, length = 3.2 units

Explanation:

Step1: Use the mid - segment theorem for slope

The mid - segment theorem states that \(DE\parallel BC\). If two lines are parallel, their slopes are equal. So the slope of \(DE\) is the same as the slope of \(BC\). Given the slope of \(BC = 0.5\).

Step2: Use the mid - segment theorem for length

The mid - segment theorem also states that \(DE=\frac{1}{2}BC\). Given \(BC = 3.2\) units. Then \(DE=\frac{1}{2}\times3.2=1.6\) units.

Answer:

D. slope = 0.5, length = 1.6 units