Answer:
To find the coordinates of point P that lies \( \frac{1}{3} \) of the way on the directed line segment AB, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint \( M \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) are:
\[ M\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]
However, since we want to find a point \( P \) that lies \( \frac{-1}{3} \) of the way from point A to point B, we need to find the coordinates of a point that is \( \frac{1}{3} \) of the way from point B to point A. We can find this point by using the midpoint formula as follows:
\[ P\left(\frac{-2 + 4}{3}, \frac{5 + 9}{3}\right) \]
\[ P\left(\frac{2}{3}, 4\right) \]
So, the coordinates of point P are \( (2/3, 4) \).
Explanation:
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