If the orthocentre and the centroid of a triangle are at (5,2,-6) and (9,6,-4) respectively, then its circumcentre is

Question

If the orthocentre and the centroid of a triangle are at (5,2,-6) and (9,6,-4) respectively, then its circumcentre is (A) (11,8,-3) (B) (8,8,-3) (C) (11,8,3) (D) (11,-8,-3)

Tardigrade Admin · Accepted Answer

We know that,
centroid of triangle is divide the orthocentre to circumcentre is ratio

2 : 1

∴ 9 = \frac{2 x + 3}{3} \Rightarrow x = 11

6 = \frac{2 y + 2}{3} \Rightarrow y = 8

- 4 = \frac{2 z - 6}{3} \Rightarrow z = - 3

∴

Circumcentre of triangle is

(11, 8, - 3)

Q. If the orthocentre and the centroid of a triangle are at $(5, 2, - 6)$ and $(9, 6, - 4)$ respectively, then its circumcentre is

$(11, 8, - 3)$

$(8, 8, - 3)$

$(11, 8, 3)$

$(11, - 8, - 3)$

We know that,
centroid of triangle is divide the orthocentre to circumcentre is ratio $2 : 1$

$∴ 9 = \frac{2 x + 3}{3} \Rightarrow x = 11$
$6 = \frac{2 y + 2}{3} \Rightarrow y = 8$
$- 4 = \frac{2 z - 6}{3} \Rightarrow z = - 3$
$∴$ Circumcentre of triangle is $(11, 8, - 3)$

Q. If the orthocentre and the centroid of a triangle are at (5,2,−6) and (9,6,−4) respectively, then its circumcentre is

(11,8,−3)

(8,8,−3)

(11,8,3)

(11,−8,−3)