A) \[(5,5),\] \[(-1,1)\]
B) \[(0,0),\]\[(4,6)\]
C) \[(0,0),\] \[(-1,1)\]
D) \[(5,5),\]\[(4,6)\]
Correct Answer: A
Solution :
| Extremities of the given diagonal are (4, 0) and (0, 6). Hence slope of this diagonal is \[-3/2\]and slope of other diagonal is 2/3. The equation of the other diagonal is |
| \[\frac{x-2}{\frac{3}{\sqrt{3}}}=\frac{y-3}{\frac{2}{\sqrt{3}}}=r\] |
| For the extremities of the diagonal, \[r=\pm \sqrt{13}.\]Hence, |
| \[x-2=\pm \,\,3,\]\[y-3=\pm \,\,2\] |
| \[x=5,-1\]and \[y=5,\]\[1\] |
| Therefore, the extremities of the diagonal are (5, 5) and \[(-\,\,1,1).\] |
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