Use the image to answer the question.

Question

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 .

Image Long DescriptionPoints upper X and upper Y appear at the ends of the line segment. Point upper R is labeled just before the arrowhead of the ray.

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

Point Z
is the endpoint of XY¯¯¯¯¯¯¯¯
. ZY=22
units

Answer 1

To analyze the relationship between point Z and line segment XY (denoted as \( \overline{XY} \)), let's break down the information:

1. It is given that ZR is the line segment bisector of \( \overline{XY} \). This means that point Z divides the line segment XY into two equal parts.
2. Since XY = 22 units, the midpoint Z will divide it into two equal lengths. Therefore, ZY will be half of 22 units.

Calculating ZY: \[ ZY = \frac{XY}{2} = \frac{22}{2} = 11 \text{ units} \]

From this, we conclude that:

• Point Z is indeed the midpoint of \( \overline{XY} \), as it is the bisector of the segment.
• And ZY equals 11 units.

Thus, the correct response is:

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