A) The point A(0, -1), B(2, 1), C(0, 3) and D(-2, 1) are vertices of a rhombus.
B) The points A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3) are vertices of a square.
C) The points A(-2, -1), B(1, 0), C(4, 3) and D(1, 2) are vertices of a parallelogram.
D) None of these
Correct Answer: C
Solution :
| [c] Here \[(a)A(0,-1),\,B(2,1),\,C(0,3),\,D(-2,1)\]. For a rhombus all four sides are equal but the diagonal are not equal, we see \[AC=\sqrt{0+{{4}^{2}}}=4\], |
| \[BD=\sqrt{{{4}^{2}}-0}=4\] |
| Since diagonals are equals therefore it is a square, not rhombus |
| [b] Here \[AB=\sqrt{{{2}^{2}}+{{(-3)}^{2}}}=\sqrt{13},\,BC\] |
| \[=\sqrt{{{6}^{2}}+{{4}^{2}}}=\sqrt{52}\] |
| Since \[AB\ne BC\] therefore it is not square. |
| [c] In this case mid point of AC is |
| \[\left( \frac{4-2}{2},\frac{3-1}{2} \right)\] or \[(1,1)\] |
| Also mid-point of diagonal \[BD\left( \frac{1+1}{2},\frac{0+2}{2} \right)\] or (1, 1) |
| Hence the points are vertices of a parallelogram. |
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