Question

If $(x,3)$ and $(3,5)$ are the extremities of a diameter of a circle with centre at $(2,y)$, then the value of $x$ and $y$ are:

• A. $x$ $=$ $1$, $y$ $=$ $4$
• B. $x$ $=$ $4$, $y$ $=$ $1$
• C. $x$ $=$ $8$, $y$ $=$ $2$
• D. None of these

Answer 1

The correct option is A $x$ $=$ $1$, $y$ $=$ $4$

The center is at the midpoint of the extremities of the diameter.

Midpoint of $(x_1,y_1),(x_2,y_2)$ is

$X=\left(\frac{x_1+x_2}{2}\right)andY=\left(\frac{y_1+y_2}{2}\right)$

So, here we have:

$\frac{x+3}{2}=2\Rightarrow x=1$

$\frac{3+5}{2}=y\Rightarrow y=4$

So option A is the right answer.