Final answer:
The distance between midpoint O of segment AB and line l is the average of the distances from A and B to line l, which calculates to be 7 inches.
Step-by-step explanation:
The distance between point A and line l is 10 inches, and the distance between point B and line l is 4 inches. To find the distance from midpoint O of segment AB to line l, we must realize that when A and B are on opposite sides of a line and we draw segment AB, line l intersects segment AB at a point we can call M. Since O is the midpoint of AB, we can consider the segment AM and BM as being made up of two segments: AO and OM, and BO and OM, respectively. OM is shared between both and AO plus BO equals AB.
Therefore, the length of OM is the average of the lengths of AM and BM. Since AM is 10 inches and BM is 4 inches (given by the distances from A and B to the line l, respectively), O, being the midpoint, is at a distance from line l that is the average of these two distances.
To calculate it: (10 inches + 4 inches) / 2 = 14 inches / 2 = 7 inches. Hence, the distance from the midpoint O to the line l is 7 inches.