Answer:
A. 1.9 units
E. 19.1 units
Step-by-step explanation:
You want the possible measures of AB if A, B, C are collinear and AC=10.5 units, BC = 8.6 units.
The attachments shows the possible arrangements of A, B, C on a line. Effectively, the order can be ABC or ACB. Point A cannot lie on segment BC because the distance AC is longer than BC.
BC = AC ± BC = 10.5 ± 8.6 = {19.1, 1.9}
BC can be 1.9 or 19.1 units, choices A and E.
The only possible value for AB, considering BC = 8.6 units and AC = 10.5 units with A, B, and C being collinear, is 1.9 units. This is deduced using the segment addition postulate.
The question involves understanding the concept of collinear points and the segment addition postulate, which states that if three points, A, B, and C, are collinear and B is between A and C, then AB + BC = AC. Given that BC = 8.6 units and AC = 10.5 units, we can deduce possible values for AB by considering various placements of these points along a line.
Considering these scenarios, the only possible value for AB with the given information is 1.9 units, which corresponds to option A. Options involving segments directly given or their sums (e.g., adding AC and BC to find a total length) are not valid as they do not conform to the possible arrangements of three collinear points with the specific distances provided.
