# Point A lies on line BC. Find the length of the segment AC if AB -23m BC-9m. How many solutions does the problem have?

July 29, 2021 | education

| Points A, B and C can be located in two ways:

1) A__B ____ C;

2) A ___ C__B.

According to the condition, the segment AB = 23 m, and the segment BC = 9 m.

The third location option (B ___ A__ C) is impossible, since a part of the whole (segment AB = 23 m) cannot be larger than the whole itself (segment BC = 9 m)

1. Consider the first option.

The segment AC is divided by point B into segments AB and BC, then its length is equal to:

AC = AB + BC;

AC = 23 + 9 = 32 (m).

2. Consider the second option.

The segment AB is divided by point C into segments AC and BC, then its length is equal to:

AB = AC + BC;

23 = AC + 9;

AC = 23 – 9 = 14 (m).

Answer: 1. AC = 32 m; 2. AC = 14 m.

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