10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

The coordinates of the point equidistant from the vertices \[O(0,0),\] \[A(6,0)\] and \[B(0,8)\] of \[\Delta AOB\] are:

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 \[=\left\{ \frac{6+0}{2},\frac{0+8}{2} \right\}\,\,=(3,4)\]