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

The coordinates of the fourth vertex of the rectangle formed by the point \[(0,0),\] \[(2,0)\] and \[(0,3)\] are:

A) \[(3,0)\]

B) \[(0,2)\]

C) \[(2,3)\]

D) \[(3,2)\]

Correct Answer: C

Solution :

[c] Let \[A(0,0),\]\[B(2,0),\] \[C(0,3)\]and \[D(0,3)\] be the vertices of the rectangle ABCD.

\[\therefore \]Mid-point of AC = Mid-point of BD

\[\Rightarrow \,\,\,\,\,\,\,\left( \frac{0+a}{2},\frac{0+b}{2} \right)\,\,=\left( \frac{2+0}{2},\,\frac{0+3}{2} \right)\]

\[\Rightarrow \,\,\,\,\,\,\,\,\frac{a}{2}=1\] and \[\frac{b}{2}=\frac{3}{2}\,\,\Rightarrow \,\,\,a=2\] and \[b=3\]

Hence, the coordinates of fourth vertex are \[(2,3)\].