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Question

The point $$(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{1}, y_{2})$$ & $$(x_{2}, y_{1})$$ are always


A
Collinear
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B
Concyclic
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C
Vertices of a square
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D
Vertices of a rhombus.
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Solution

The correct option is B Concyclic
Let the coordinates be denoted as $$A(x_1,y_2)$$, $$B(x_2,y_2)$$, $$C(x_2,y_1)$$ and $$D(x_1,y_1)$$
Plot the given points on a graph as above,
It is not necessary that
$$|x_2-x_1|=|y_2-y_1|$$
With $$(x_2,y_1)$$ and $$(x_1,y_2)$$ as ends of diameter $$\angle ABC=90^{\circ}$$ and $$\angle ADC=90^{\circ}$$
$$\therefore ABCD$$ are concyclic.
So, $$\text{B}$$ is the correct option.

1940934_1415967_ans_cfacbeab028b474f8369d893f1f639f2.png

Mathematics

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