Question

select all that bisect \\(\overline{qt}\\).

select one or more:
a. \\(p\\)
b. \\(\overleftrightarrow{vs}\\)
c. \\(\overline{pt}\\)
d. \\(\overline{qp}\\)
e. \\(\overline{sp}\\)
f. \\(\overleftrightarrow{up}\\)

Explanation:

Identify the segment to bisect

Using the Segment Bisector knowledge point

$$ \text{Target segment: } \overline{QT} $$

$$ \text{Midpoint condition: } QP = PT $$

$$ \text{From tick marks: } QP = PT \implies P \text{ is the midpoint of } \overline{QT} $$

Determine bisecting geometric figures

Using the Segment Bisector knowledge point

$$ \text{Any point, line, ray, or segment passing through midpoint } P \text{ bisects } \overline{QT}. $$

$$ \text{Evaluate options:} $$

• \(P\): Point \(P\) is the midpoint itself, so it bisects \(\overline{QT}\).
• \(\overleftrightarrow{VS}\): Line \(\overleftrightarrow{VS}\) passes through \(P\), so it bisects \(\overline{QT}\).
• \(\overline{PT}\): Segment \(\overline{PT}\) is a part of \(\overline{QT}\) starting at \(P\), but does not cross or bisect it.
• \(\overline{QP}\): Segment \(\overline{QP}\) is a part of \(\overline{QT}\) ending at \(P\), but does not bisect it.
• \(\overrightarrow{SP}\): Ray \(\overrightarrow{SP}\) starts at \(S\) and passes through \(P\), so it bisects \(\overline{QT}\).
• \(\overrightarrow{UP}\): Ray \(\overrightarrow{UP}\) starts at \(U\) and passes through \(P\), so it bisects \(\overline{QT}\).

Answer:

• a. \(P\) (Correct answer)
• b. \(\overleftrightarrow{VS}\) (Correct answer)
• c. \(\overline{PT}\)
• d. \(\overline{QP}\)
• e. \(\overrightarrow{SP}\) (Correct answer)
• f. \(\overrightarrow{UP}\) (Correct answer)