Sure, of course! Let’s go through each part of the question step-by-step:
### 1. Finding the Length of the Segment
To find the length of the segment, you subtract the coordinates of the two points and take the absolute value.
### 2. Statement Taken to be True Without Proof
A statement which is taken to be true without proof is called an axiom.
### 3. Point where Two Objects Meet or Cross
The point where two objects (such as lines) meet or cross is called the vertex.
### 4. Collinear Points Statement
If three points [tex]\( A, B \)[/tex], and [tex]\( C \)[/tex] are collinear, and [tex]\( B \)[/tex] is between [tex]\( A \)[/tex] and [tex]\( C \)[/tex], then the relationship between the segments is expressed by the equation
[tex]\[ AB + BC = AC \][/tex]
### 5. Line Segment Description
A piece of a line that connects two points and has definite end points is called a line segment.
Thus, putting together the details:
- To find the length of the segment by subtracting the coordinate and taking the absolute value.
- A statement which is taken to be true without proof is an axiom.
- The point where two objects meet or cross is the vertex.
- For collinear points [tex]\( A, B \)[/tex], and [tex]\( C \)[/tex] with [tex]\( B \)[/tex] between [tex]\( A \)[/tex] and [tex]\( C \)[/tex]: [tex]\( AB + BC = AC \)[/tex].
- A piece of a line that connects two points and has definite end points is a line segment.
