Question

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

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

Solution

## The correct option is B ConcyclicLet 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.Mathematics

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