A) \[\sqrt{13}\]units
B) \[\sqrt{50}\]units
C) \[2\sqrt{28}\]units
D) \[\sqrt{58}\]units
Correct Answer: D
Solution :
Given, TU is median of PQ. \[\Rightarrow \] U is mid point of PQ. Also, R is mid point of QS. (Given) \[\therefore \] Coordinates of \[Q=(6-6,10-5)=(0,5)\] Q is mid point of PS (Given) \[\therefore \] Coordinates of \[P=(0-6,\,\,10-5)=(-6,\,5)\]. Hence, coordinates of \[U=\left( \frac{-6+0}{2},\frac{5+5}{2} \right)=(-3,5)\] \[\therefore \] Length of median TU \[=\sqrt{{{(-3-4)}^{2}}+{{(5-8)}^{2}}}=\sqrt{49+9}=\sqrt{58}\] units.
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