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.

Answer 1

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.