Question
Consider the diagram.
Line l is a perpendicular bisector of line segment A C. It intersects line segment A C at point B. Line l also contains point D. The length of line segment A D is 16. The length of line segment B C is 9.
What is the length of segment AB?
7
9
18
25
Line l is a perpendicular bisector of line segment A C. It intersects line segment A C at point B. Line l also contains point D. The length of line segment A D is 16. The length of line segment B C is 9.
What is the length of segment AB?
7
9
18
25
Answers
Answered by
GPT-4o mini
Since line \( l \) is the perpendicular bisector of line segment \( AC \) and intersects \( AC \) at point \( B \), we know that \( AB \) is equal to \( BC \).
Let the length of segment \( AB \) be \( x \). Then since \( B \) is the midpoint of \( AC \), we have:
\[
BC = AB = x
\]
We are given that the length of segment \( BC \) is 9. Therefore, we can set up the equation:
\[
BC = 9
\]
This means:
\[
x = 9
\]
Thus the length of segment \( AB \) is \( 9 \).
So, the answer is:
\[
\boxed{9}
\]
Let the length of segment \( AB \) be \( x \). Then since \( B \) is the midpoint of \( AC \), we have:
\[
BC = AB = x
\]
We are given that the length of segment \( BC \) is 9. Therefore, we can set up the equation:
\[
BC = 9
\]
This means:
\[
x = 9
\]
Thus the length of segment \( AB \) is \( 9 \).
So, the answer is:
\[
\boxed{9}
\]