Which of the points given divide the line segment ab in the ratio 2: 3?

The correct answer is Choice D, (5, 7).

First, we need to identify the slope from A to B.
It will be -5/-5. In other words, to go from A to B, we move down 5 spaces and left 5 spaces.

If we are going to divide the segment, we are not going to move all 5 spaces in each direction. 

Since we are looking for a 2:3 ratio, we are only moving 2 out of the total of 5 spaces. It is 2 over 5, because 2 + 3 makes a total of 5.

Therefore, we only move down 2 and left 2 spaces from Point A. That will put us at the point (5, 7).