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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

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

b. Point Z is the center point of XY¯¯¯¯¯¯¯¯. ZY=22 units

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

d. Point Z is the center point of XY¯¯¯¯¯¯¯¯. ZY=11 units.

1 answer

To determine how point Z relates to segment XY and calculate the length of ZY, let's analyze the information given.

  1. Bisector: Since segment ZR is described as the "line segment bisector" of segment XY, this indicates that point Z is the midpoint of segment XY.

  2. Length of XY: We're given that the length of XY is 22 units.

Now, since Z is the midpoint of XY, the length from Z to either endpoint (X or Y) will be half the total length of XY.

Calculating ZY:

  • Length of XY = 22 units
  • Since Z is the midpoint, ZY (which is half of XY) = 22 units / 2 = 11 units.

Given these points, we can conclude:

  • Point Z is the midpoint of XY.
  • The length ZY = 11 units.

So the correct response is:

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