Consider the following figure of line $ \overline{\mathrm{MN}} $. Say whether following statements are true or false in context of the given figure.
(a) $ \mathrm{Q}$
To do:
We have to find whether the given statements are true or false.
Solution:
(a) We can observe that points \( \mathrm{Q}, \mathrm{M}, \mathrm{O}, \mathrm{N}, \mathrm{P} \) are on the line \( \mathrm{MN} \).
The given statement is true.
(b) We can observe that \( \mathrm{M}, \overline{\mathrm{O}}, \mathrm{N} \) are points on the line segment \( \overline{\mathrm{MN}} \).
The given statement is true.
(c) We can observe that \( \mathrm{M} \) and \( \mathrm{N} \) are end points of the line segment \( \overline{\mathrm{MN}} \).
The given statement is true.
(d) We can observe that \( \mathrm{O} \) and \( \mathrm{P} \) are end points of line segment \( \overline{\mathrm{OP}} \).
The given statement is false.
(e) We can observe that \( M \) is not one of the end points of line segment \( \overline{\mathrm{QO}} \).
The end points of line segment \( \overline{\mathrm{QO}} \) are $Q$ and $O$.
The given statement is false.
(f) We can observe that point \( \mathrm{M} \) is not on the ray \( \overrightarrow{\mathrm{OP}} \).
The given statement is false.
(g) Ray \( \overrightarrow{\mathrm{OP}} \) starts at point $O$
Ray \( \overrightarrow{\mathrm{QP}} \) starts at point $Q$
The given statement is true.
(h) Ray \( \overrightarrow{\mathrm{OP}} \) starts at point $O$
Ray \( \overrightarrow{\mathrm{OM}} \) starts at point $O$ but is in opposite direction of the above ray.
The given statement is false.
(i) Ray \( \overrightarrow{\mathrm{OP}} \) starts at point $O$
Ray \( \overrightarrow{\mathrm{OM}} \) starts at point $O$ but is in opposite direction of the above ray.
The given statement is false.
(j) We can observe that \( \mathrm{O} \) is the initial point of \( \overrightarrow{\mathrm{OP}} \).
The given statement is false.
(k) We can observe that \( \mathrm{N} \) is the initial point of \( \overrightarrow{\mathrm{NP}} \) and \( \mathrm{N} \) is also the initial point of \( \overrightarrow{\mathrm{NM}} \)
The given statement is true.
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