#1**+2 **

If the slope of line DE = the slope of line BC, then DE is parallel to BC.

D is the midpoint of AB, so D = \((\frac{4+2}{2},\frac{6-2}{2})\) = (3, 2)

E is the midpoint of AC, so E = \((\frac{4-2}{2},\frac{6-4}{2})\) = (1, 1)

slope of DE = \(\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{2-1}{3-1}\,=\,\frac{1}{2}\)

slope of BC = \(\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{-4+2}{-2-2}\,=\,\frac{-2}{-4}\,=\,\frac{1}{2}\)

Since the slope of DE and the slope of BC both equal \(\frac12\) , DE is parallel to BC.

Here's a graph to check: https://www.desmos.com/calculator/5k2mf7pbjj

hectictar May 11, 2019

#1**+2 **

Best Answer

If the slope of line DE = the slope of line BC, then DE is parallel to BC.

D is the midpoint of AB, so D = \((\frac{4+2}{2},\frac{6-2}{2})\) = (3, 2)

E is the midpoint of AC, so E = \((\frac{4-2}{2},\frac{6-4}{2})\) = (1, 1)

slope of DE = \(\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{2-1}{3-1}\,=\,\frac{1}{2}\)

slope of BC = \(\frac{y_2-y_1}{x_2-x_1}\,=\,\frac{-4+2}{-2-2}\,=\,\frac{-2}{-4}\,=\,\frac{1}{2}\)

Since the slope of DE and the slope of BC both equal \(\frac12\) , DE is parallel to BC.

Here's a graph to check: https://www.desmos.com/calculator/5k2mf7pbjj

hectictar May 11, 2019