Question

1. a) name the line that contains the point q. b) name the two opposite rays. c) name the end point of \overrightarrow{qt}. d) name all the points that lie on the \overleftrightarrow{st}.

Explanation:

Step1: Identify lines containing Q

Lines are determined by two points. From the diagram, lines \( \overleftrightarrow{PR}\), \( \overleftrightarrow{UT}\), \( \overleftrightarrow{ST}\) pass through \(Q\).

Step2: Find opposite rays

Opposite rays share an endpoint and form a straight line. \( \overrightarrow{SQ}\) and \( \overrightarrow{TQ}\) share endpoint \(Q\) and form line \(ST\).

Step3: Determine endpoint of \( \overrightarrow{QT}\)

A ray has one endpoint. For \( \overrightarrow{QT}\), the endpoint is \(Q\).

Step4: List points on \( \overleftrightarrow{ST}\)

Points on a line are all points that lie on it. From the diagram, points \(S\), \(Q\), \(T\) lie on \( \overleftrightarrow{ST}\).

Answer:

a) \( \overleftrightarrow{PR}\), \( \overleftrightarrow{UT}\), \( \overleftrightarrow{ST}\)
b) \( \overrightarrow{SQ}\) and \( \overrightarrow{TQ}\)
c) \(Q\)
d) \(S\), \(Q\), \(T\)