Three vertices of a rhombus are \[(2,-1),\]\[(3,4)\]and \[(-\,\,2,3).\]Find the fourth vertex. |
A) \[(1,2)\]
B) \[(3,2)\]
C) \[(-\,\,2,-\,\,3)\]
D) \[(-\,\,3,\,\,-2)\]
E) \[(2,3)\]
Correct Answer: D
Solution :
Let coordinate of D be \[(x,y)\]and M be the intersection point of diagonals AC and BD. Since, M is the mid-point of AC. \[\therefore \]Coordinate of \[M=\left( \frac{-\,2+2}{2},\frac{-1+3}{2} \right)=(0,1)\] Also, M is the mid-point of BD. \[\therefore \]Coordinate of \[M=\left( \frac{x+3}{2},\frac{y+4}{2} \right)\] \[\therefore \] \[\frac{x+3}{2}=0\]\[\Rightarrow \]\[x=-\,\,3\] and \[\frac{y+4}{2}=1\]\[\Rightarrow \]\[y=-\,\,2\]You need to login to perform this action.
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