Points A (29.4), B (93.5) and C. The distance from point C to point A is equal to 25.6 unit segments.

| June 27, 2021 | education

Points A (29.4), B (93.5) and C. The distance from point C to point A is equal to 25.6 unit segments. Find AB, AC and BC. How many solutions does the problem have?

Consider the coordinate ray Ox, where points A (29.4) and B (93.5) are marked. In addition, point C is located on it, the distance from which to point A is equal to 25.6 unit segments. It is required to find AB, AC and BC. First of all, let’s answer the question posed: The problem has two solutions.
First of all, we find the length of the segment AB as the difference in coordinates between the extreme points of the segment: AB = 93.5 – 29.4 = 64.1. The length of the segment AB was calculated unambiguously. The length of the segment AC can also be determined unambiguously. According to the terms of the assignment, AC = 25.6. However, the length of the aircraft segment cannot be determined unambiguously. The fact is that point C can be located at a distance of 25.6 unit segments from point A, in two ways: a) point C is located to the left of point A and b) point C is located to the right of point A. Consider both cases separately.
In case a), the coordinate of point C will be 29.4 – 25.6 = 3.8. Then BC = 93.5 – 3.8 = 89.7. However, in case b) the coordinate of point C will be equal to 29.4 + 25.6 = 55. Therefore, BC = 93.5 – 55 = 38.5.
Answers: a) AB = 64.1, AC = 25.6 and BC = 89.7; b) AB = 64.1, AC = 25.6 and BC = 38.5.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.