is it possible that the points a, b,c are collinear but AB + BC not equal AC
only if b is not between a and c. The way the points are listed, one expects a, then b, then c, but maybe it's a-c-b and the points a,b,c are still collinear.
I think the desired answer is No.
Yes, it is possible for three points A, B, and C to be collinear but for the sum of the lengths of two of the line segments (AB + BC) to be not equal to the length of the third line segment (AC). Let me explain how this could happen.
Three points A, B, and C are collinear if they all lie on the same straight line. In other words, the slope between any two of the points is the same. Let's assume that A, B, and C are collinear, which means they lie on a straight line.
Now, let's consider the lengths of the line segments AB, BC, and AC. Since A, B, and C are collinear, the length of AC should be equal to the sum of the lengths of AB and BC (AC = AB + BC) if they are collinear.
However, it is possible to have a situation where the sum of the lengths of AB and BC is not equal to the length of AC. This can happen if there is some type of distortion or transformation applied to the line segments after they are drawn. For example, if the line segments AB and BC are stretched or compressed unevenly, the sum of their lengths might not be equal to the length of AC.
In summary, while it is unlikely to occur naturally, it is possible for the points A, B, and C to be collinear but for the lengths of AB + BC to not be equal to AC if some form of transformation has been applied to the line segments after they were drawn.