Asked by PJ
Line segment XY¯¯¯¯¯¯¯¯ is a perpendicular bisector of segment AB¯¯¯¯¯¯¯¯ , with the two segments meeting at point O . What is true about OB¯¯¯¯¯¯¯¯ ? (1 point)
It has the same length as AO¯¯¯¯¯¯¯¯ .
It has the same length as OY¯¯¯¯¯¯¯¯ .
It has the same length as XO¯¯¯¯¯¯¯¯ .
It has the same length as XB¯¯¯¯¯¯¯¯ .
It has the same length as AO¯¯¯¯¯¯¯¯ .
It has the same length as OY¯¯¯¯¯¯¯¯ .
It has the same length as XO¯¯¯¯¯¯¯¯ .
It has the same length as XB¯¯¯¯¯¯¯¯ .
Answers
GPT-4o mini
Since line segment XY is the perpendicular bisector of segment AB, we can conclude several properties about the lengths of the segments involved:
1. Because XY is a bisector, it divides segment AB into two equal parts at point O. This means:
\[
AO = OB
\]
Therefore, OB has the same length as AO.
2. Since XY is perpendicular to AB at point O, and both segments are meeting at O, the relationship between the lengths of segments XO and OY is not directly related to the length of OB.
3. The lengths of segments X and B do not have a direct relationship through the property of line segment bisectors unless further information on the configuration is given, but OB does not equal XO or XB in general.
Thus, the correct statement is:
**It has the same length as AO.**
1. Because XY is a bisector, it divides segment AB into two equal parts at point O. This means:
\[
AO = OB
\]
Therefore, OB has the same length as AO.
2. Since XY is perpendicular to AB at point O, and both segments are meeting at O, the relationship between the lengths of segments XO and OY is not directly related to the length of OB.
3. The lengths of segments X and B do not have a direct relationship through the property of line segment bisectors unless further information on the configuration is given, but OB does not equal XO or XB in general.
Thus, the correct statement is:
**It has the same length as AO.**