Question

If the co ordinates of vertices of a triangle are $(0,5),(1,4)$ and $\left(2.5\right)$ then the co-ordinate of circumcenter will be.

• A. $(1,5)$
• B. $(\frac{3}{2},\frac{9}{2})$
• C. $(1,4)$
• D. $(1,\frac{14}{3})$

Answer 1

The correct option is D $(1,\frac{14}{3})$

Vertices

$A(0,5),B(1,4),C(2,5)$

$AB=\sqrt{{(0-1)}^2+{(5-4)}^2}=\sqrt{2}$

$BC=\sqrt{{(1-2)}^2+{(4-5)}^2}=\sqrt{2}$

$CA=\sqrt{{(2-4)}^2+{(5-5)}^2}=\sqrt{2}$

Triangle is equilateral

So, circumcenter will coincide with the centroid

Centroid=C.S$=\frac{0+2+2}{3},\frac{5+4+5}{3}$

$=(1,\frac{14}{3})$