Question

name the following line six different ways.
which of the following is not a way to name the line?
a. \\(\overleftrightarrow{pq}\\)
b. \\(\overleftrightarrow{oq}\\)
c. \\(\overleftrightarrow{p}\\)
d. \\(\overleftrightarrow{op}\\)
e. \\(\overleftrightarrow{po}\\)
f. \\(\overleftrightarrow{qp}\\)
g. \\(\overleftrightarrow{qo}\\)

Explanation:

Identify valid naming conventions for a line

$$ \text{A line is named using any two distinct points on the line with a double-headed arrow above them: } \overleftrightarrow{XY} $$

$$ \text{Points on the line: } \{O, P, Q\} $$

$$ \text{Possible combinations of two distinct points: } \{O,P\}, \{O,Q\}, \{P,Q\} $$

List all six valid names for the line

$$ \overleftrightarrow{OP}, \overleftrightarrow{PO}, \overleftrightarrow{OQ}, \overleftrightarrow{QO}, \overleftrightarrow{PQ}, \overleftrightarrow{QP} $$

Evaluate the given options against valid names

$$
LATEXBLOCK0
$$

Answer:

• A. \(\overleftrightarrow{PQ}\)
• B. \(\overleftrightarrow{OQ}\)
• C. \(\overleftrightarrow{P}\) (Correct answer)
• D. \(\overleftrightarrow{OP}\)
• E. \(\overleftrightarrow{PO}\)
• F. \(\overleftrightarrow{QP}\)
• G. \(\overleftrightarrow{QO}\)