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Line segment upper X upper Y has a nearly vertical orientation, sloping downward steeply from left to right. Ray upper Z upper R extends rightward and upward from midpoint upper Z on the line segment upper X upper Y .

Aleph constructed ZR−→− , a line segment bisector of XY¯¯¯¯¯¯¯¯ . How does point Z relate to XY¯¯¯¯¯¯¯¯ ? If XY=22 units, what is ZY ?

(1 point)
Responses

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.
Point upper Z is the midpoint of Modifying above upper X upper Y with bar . upper Z upper Y equals 11 units.

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.

1 answer

To determine the relationship of point Z to line segment \( \overline{XY} \) and the value of \( ZY \), we can analyze the provided information.

  1. Understanding Midpoints: The point Z is constructed as the midpoint of the line segment \( \overline{XY} \). Since it is the midpoint, the lengths of segment \( ZY \) will be half of the total length of \( XY \).

  2. Calculating ZY: If the length of \( XY \) is given as 22 units, and point Z is the midpoint, then: \[ ZY = \frac{XY}{2} = \frac{22 \text{ units}}{2} = 11 \text{ units} \]

  3. Conclusion: Point Z is indeed the midpoint of \( \overline{XY} \), and therefore,

    • Point Z is the midpoint of \( \overline{XY} \).
    • The length \( ZY \) is 11 units.

Based on this analysis, the correct response is: Point Z is the midpoint of \( \overline{XY} \). ZY = 11 units.