Discussion

Find the coordinates of the point that is two-thirds of the way from A(-4, 3) to B(5, 9).

Answer: A

A point that is two-thirds of the way from A to B divides the line segment AB in the ratio 2:1.

Using the section formula with \(m_1=2\) and \(m_2=1\):

x = \(\frac{2(5) + 1(-4)}{2+1} = \frac{10-4}{3} = \frac{6}{3} = 2\)

y = \(\frac{2(9) + 1(3)}{2+1} = \frac{18+3}{3} = \frac{21}{3} = 7\)

The coordinates are (2, 7).

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