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
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