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 \[(2,3)\]. |
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