• question_answer 6) Consider the following figure of line $\overset{\leftrightarrow }{\mathop{MN.}}\,$Say whether following statements are true or false in context of the given figure. (a) Q, M, O, N, P are points on the line $\overset{\leftrightarrow }{\mathop{MN.}}\,$ (b) M, O, N are points on a line segment $\overline{MN}.$ (c) M and N are end points of line segment $\overline{MN}.$ (d) O and N are end points of line segment $\overline{OP}.$ (e) M is one of the end points of line segment$\overline{QO}.$ (f) M is point on ray $\overline{OP}.$ (g) Ray $\overset{\to }{\mathop{OP}}\,$ is different from ray $\overset{\to }{\mathop{QP}}\,.$ (h) Ray $\overset{\to }{\mathop{OP}}\,$is same as ray$\overset{\to }{\mathop{OM}}\,.$ (i) Ray$\overset{\to }{\mathop{OM}}\,$is not opposite to ray $\overset{\to }{\mathop{OP}}\,.$ (j) O is not an initial point of$\overset{\to }{\mathop{OP}}\,.$ (k) N is the initial point of $\overset{\to }{\mathop{NP}}\,$ and $\overset{\to }{\mathop{NM}}\,.$

(a) True, because points M, O and N lie on the line $\overset{\leftrightarrow }{\mathop{MN}}\,$and points Q and Plie on the extended portion of $\overset{\leftrightarrow }{\mathop{MN}}\,$ on both sides. (b) True, because points M, O, N lie on the line segment $\overline{MN}.$ (c) True, because M to N is the shortest route of line segment $\overline{MN}.$ (d) False, because it is clear from figure that point N is between O and P. (e) False, because it is clear from figure that point M is between Q and O. (f) False, because M is outside from ray $\overset{\to }{\mathop{OP}}\,.$ (g) True, because all the rays have their own existence. (h) False, because rays $\overset{\to }{\mathop{OP}}\,$ and $\overset{\to }{\mathop{OM}}\,$ are in opposite directions. (i) True, because it is clear from figure that rays $\overset{\to }{\mathop{OM}}\,$ and $\overset{\to }{\mathop{OP}}\,$ are opposite. (j) False, because it is clear from figure that point O is the initial point of $\overset{\leftrightarrow }{\mathop{OP}}\,.$ (k) True, because it is clear from figure that line segment $\overline{NP}$ and $\overline{NM}$start from point N.