Answer: The point (5, 6) would divide the line segment so it is in the ratio of 3:5.
If the ratio of the line segment needs to be 3:5, that means the point will be at the 3/8 distance mark of the line segment. Because there are 8 total parts if the ratio is 3:5 (3 + 5 = 8).
The slope from (2, 9) to (10, 1) is -8/8. So our point would only move 3/8 of that distance. If we multiply -8 and 8 by 3/8, we have -3 and 3.
That means our point must fall 3 and move to the 3 spaces from our starting point of (2, 9). That will put us at (5, 6).
