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

Explanation:

Step1: Use the Mid - segment Theorem (Slope)

The mid - segment of a triangle (\(DE\)) is parallel to the third side (\(BC\)). Parallel lines have the same slope. Since the slope of \(BC\) is \(0.5\), the slope of \(DE\) is also \(0.5\).

Step2: Use the Mid - segment Theorem (Length)

The length of the mid - segment of a triangle is half the length of the third side. Given the length of \(BC = 3.2\) units. Then the length of \(DE=\frac{1}{2}\times BC\). Substitute \(BC = 3.2\) into the formula: \(DE=\frac{1}{2}\times3.2 = 1.6\) units.

Answer:

A. slope = 0.5, length = 1.6 units