Question

Aleph constructed ZR−→−, a line segment bisector of XY¯¯¯¯¯¯¯¯. How does point Z relate to XY¯¯¯¯¯¯¯¯? If XY=22 units, what is ZY? which is the true correct answer solve it and tell me why

(1 point)
Responses

Point Z is the midpoint of XY¯¯¯¯¯¯¯¯. ZY=22 units.
Point upper Z is the midpoint of Modifying above upper X upper Y with bar . upper Z upper Y equals 22 units.

Point Z is the center point of XY¯¯¯¯¯¯¯¯. ZY=11 units.
Point upper Z is the center point of Modifying above upper X upper Y with bar . upper Z upper Y equals 11 units.

Point Z is the center point of XY¯¯¯¯¯¯¯¯. ZY=22 units
Point upper Z is the center point of Modifying above upper X upper Y with bar . upper Z upper Y equals 22 units

Point Z is the midpoint of XY¯¯¯¯¯¯¯¯. ZY=11 units.

Answer 1

To solve the problem, let's analyze the relationships involved:

1. **Understanding the Line Segment and Midpoint**:
- Line segment \( XY \) has a length of 22 units.
- A bisector (or midpoint) divides the segment into two equal parts.

2. **Using the Definition of a Midpoint**:
- The midpoint \( Z \) of a segment \( XY \) is defined as the point that divides \( XY \) into two equal segments.
- Therefore, if \( XY = 22 \) units, then each half (from \( X \) to \( Z \) and from \( Z \) to \( Y \)) will be:
\[
ZY = \frac{XY}{2} = \frac{22 \text{ units}}{2} = 11 \text{ units}
\]

3. **Analyzing the Given Options**:
- **Option 1**: Point Z is the midpoint of XY; ZY = 22 units. **(Incorrect)**
- **Option 2**: Point Z is the midpoint of XY; ZY = 22 units. **(Incorrect)**
- **Option 3**: Point Z is the center point of XY; ZY = 11 units. **(Correct)**
- The terms "midpoint" and "center point" mean the same in this context.
- **Option 4**: Point Z is the midpoint of XY; ZY = 11 units. **(Also Correct)**

Both option 3 and option 4 indicate that point Z is the midpoint of segment XY and accurately express that ZY equals 11 units.

**Conclusion**: The best response is that:
- Point Z is the midpoint of \( XY \)
- \( ZY = 11 \) units.

So, the correct answer would be:
**Point Z is the midpoint of XY; ZY = 11 units.**