Let's interpret the descriptions given by Olivia and Makayla logically. We can imagine the dashed line and line [tex]\(RW\)[/tex] to visualize these relationships clearly.
### Olivia's Description
Olivia states that the dashed line divides line [tex]\(RW\)[/tex] in half. This implies that the dashed line bisects [tex]\(RW\)[/tex], meaning it intersects [tex]\(RW\)[/tex] at the midpoint. If we denote [tex]\(R\)[/tex] and [tex]\(W\)[/tex] as the endpoints of the line segment, the dashed line cuts the segment such that each half is of equal length. For example, if [tex]\(RW\)[/tex] measures 4 units, the dashed line intersects at the 2-unit mark, creating two segments each of 2 units.
### Makayla's Description
Makayla's description mentions that the dashed line makes a right angle with line [tex]\(RW\)[/tex]. This means that the dashed line is perpendicular to [tex]\(RW\)[/tex]. The geometric implication of this is that the angle between the dashed line and [tex]\(RW\)[/tex] is 90 degrees.
### Combined Interpretation
When we combine both students' descriptions, the dashed line not only bisects [tex]\(RW\)[/tex] but does so in a perpendicular manner. This means that not only is line [tex]\(RW\)[/tex] divided into two equal lengths, but the intersection forms a right angle. This setup is characteristically referred to as the relationship where the dashed line acts as a perpendicular bisector of line [tex]\(RW\)[/tex].
### Conclusion
To encapsulate the joint descriptions provided by Olivia and Makayla in geometric terms:
1. Olivia's observation of the dashed line bisecting [tex]\(RW\)[/tex] at its midpoint leads us to recognize a division into equal segments.
2. Makayla's observation adds the critical information that this intersection occurs at a 90-degree angle.
Thus, we conclude that:
- The dashed line is a perpendicular bisector of line [tex]\(RW\)[/tex].
This relationship ensures that [tex]\(RW\)[/tex] is cut into two equal parts at a right angle.
