Question

The circum centre of the triangle formed by the points $(2,5,1),(1,4,-3)$ and $(-2,7,-3)$ is

• A. $(6,0,1)$
• B. $(0,6,-1)$
• C. $(-1,6,2)$
• D. $(6,1,-2)$

Answer 1

Answer: (B)

$(0,6,-1)$

Let the points $A(2,5,1)B(1,4,-3)$ and $C(-2,7,-3)$
Now using distance formula in $3D$, we have
$AB=$$\sqrt{18}$, $BC=$$\sqrt{18}$, and $AC=$$\sqrt{36}$
Since, ${AB}^2+{BC}^2$$=$${AC}^2$
Hence, it is right angle triangle and as we know that the circumcentre of right angled triangle is at the midpoint of hypotenuse i.e $AC$.
Therefore by using section formula (1:1), circumcentre $=(0,6,-1)$