Question

The circumcentre of the triangle formed by $(2,-5),$ $(2,7),$ $(4,7)$ is

• A. $(3,1)$
• B. $(2,7)$
• C. $(3,-1)$
• D. $(-3,-1)$

Answer 1

The correct option is A $(3,1)$

$A(2,-5),B(2,7),C(4,7)$ are the vertices of the triangle.
Here $x$-coordinate of $A=x$-coordinate of $B$
It implies that $AB$ is parallel to $y$-axis, and is vertical side.
$y$-coordinate of $B=y$-coordinate of $C$
It implies that $BC$ is parallel to $x$-axis, and is horizontal side.

$\Rightarrow AC$ will be the hypotenuse of the right-angled triangle $△ABC$
$\therefore$ Circumcentre will be the mid-point of $AC=(\frac{4+2}{2},\frac{7-5}{2})=(3,1)$