Question
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) Responses It has the same length as AO¯¯¯¯¯¯¯¯ . It has the same length as line segment cap A cap o. It has the same length as OY¯¯¯¯¯¯¯¯ . It has the same length as line segment cap o cap y. It has the same length as XB¯¯¯¯¯¯¯¯ . It has the same length as line segment cap x cap b. It has the same length as XO¯¯¯¯¯¯¯¯ . It has the same length as line segment cap x cap o.
Answers
GPT-4o mini
Given that line segment XY is the perpendicular bisector of segment AB, and O is the point where the two segments intersect, we can derive several important properties:
1. By definition of a perpendicular bisector, it divides the segment AB into two equal parts. This means:
\[
AO = OB
\]
Thus, the length of OB is the same as the length of AO.
2. Since XY is perpendicular to AB, it is not specifically relevant to the lengths of segments OY or XB in this context.
Therefore, the correct statement regarding the lengths involving segment OB is:
- **It has the same length as AO.**
So, the appropriate option from your list would be:
- **It has the same length as AO.**
1. By definition of a perpendicular bisector, it divides the segment AB into two equal parts. This means:
\[
AO = OB
\]
Thus, the length of OB is the same as the length of AO.
2. Since XY is perpendicular to AB, it is not specifically relevant to the lengths of segments OY or XB in this context.
Therefore, the correct statement regarding the lengths involving segment OB is:
- **It has the same length as AO.**
So, the appropriate option from your list would be:
- **It has the same length as AO.**