A) \[(2,3)\]
B) \[(3,4)\]
C) \[(-3,4)\]
D) \[(2,-3)\]
Correct Answer: B
Solution :
[b]\[OA=\sqrt{{{(6-0)}^{2}}+{{(0-0)}^{2}}}=6\] units |
\[OB=\sqrt{{{(0-0)}^{2}}+{{(8-0)}^{2}}}=8\] units |
and\[AB=\sqrt{{{(0-6)}^{2}}+{{(8-0)}^{2}}}\sqrt{36+64}\] |
\[=\sqrt{100}=10\] units |
\[A{{B}^{2}}=O{{A}^{2}}+O{{B}^{2}}\] |
\[\therefore \,\,\Delta AOB\]is a right angle. |
So, mid-point of hypotenuse of \[\Delta AOB\] is the point which is equidistant from the given vertices. |
\[\therefore \] Required point \[=\left\{ \frac{6+0}{2},\frac{0+8}{2} \right\}\,\,=(3,4)\] |
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