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Problem 639

Prove that points \(\mathrm{A}(2,3), \mathrm{B}(4,4)\), and \(\mathrm{C}(8,6)\) are collinear.

Expert verified

The points A(2,3), B(4,4), and C(8,6) are collinear. This is proven by calculating the slopes of lines AB, AC, and BC. The slope of AB is \(\frac{1}{2}\), calculated using the slope formula \(\frac{y_2 - y_1}{x_2 - x_1}\) (specifically, \(\frac{4-3}{4-2} = \frac{1}{2}\)). The same calculation gives the slope of AC as \(\frac{1}{2}\) (from \(\frac{6-3}{8-2}\)) and the slope of BC as \(\frac{1}{2}\) (from \(\frac{6-4}{8-4}\)). As all three slopes are equal, the points are collinear.

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Chapter 36

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