Question

In the diagram below, points A and B are 3 inches apart. Try to find two points that are 1 inch from point A

and 1.5 inches from point B. Why do you think it is impossible to find such points?

A______________________B
3"

Answer 1

It is impossible to find two points that are both 1 inch and 1.5 inches from the point A simultaneously as shown in the following proof

From segment addition postulate given a point C that is between the points of a segment AB, we have;

AC + CB = AB

Therefore, where AC = 1 inch and CB = 1.5 inches, we have;

AC + CB = 1 inch + 1.5 inches = 2.5 inches ≠ AB = 3 inches

However it is possible to find two points in which one of the points is 1 inch from the point A while the other point is 1.5 inches from the point B

Explanation: