Centroid of a triangle $ABC$ is at the point $(1, 1, 1)$. If the co-ordinates of $A$ and $B$ are $(3, -5, 7)$ and $(-1, 7, -6)$ respectively then the co-ordinates of $C$

(a) $(1, 1, 1)$
(b) $(1, 1, 4)$
(c) $(1, 1, 1)$
(d) None of these

Question

Centroid of a triangle $ABC$ is at the point $(1, 1, 1)$. If the co-ordinates of $A$ and $B$ are $(3, -5, 7)$ and $(-1, 7, -6)$ respectively then the co-ordinates of $C$

(a) $(1, 1, 1)$
(b) $(1, 1, 4)$
(c) $(1, 1, 1)$
(d) None of these

Accepted Answer

>

> [!TLDR]
> $C=(1,1,2)$, not in the list, so option (d).
>
> Centroid $G=\left(\frac{x_A+x_B+x_C}{3},\frac{y_A+y_B+y_C}{3},\frac{z_A+z_B+z_C}{3}\right)=(1,1,1)$ (NCERT Class 11 3D Geometry).
> …

Plane	Equation	Description
$xy$ -plane	$z = 0$	the floor — all points with zero height
$yz$ -plane	$x = 0$	one wall — all points with zero $x$
$zx$ -plane	$y = 0$	the other wall — all points with zero $y$

Q.Centroid of a triangle $ABC$ is at the point $(1, 1, 1)$ . If the co-ordinates of $A$ and $B$ are $(3, -5, 7)$ and $(-1, 7, -6)$ respectively then the co-ordinates of $C$

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Q.Centroid of a triangle ABCABCABC is at the point (1,1,1)(1, 1, 1)(1,1,1). If the co-ordinates of AAA and BBB are (3,−5,7)(3, -5, 7)(3,−5,7) and (−1,7,−6)(-1, 7, -6)(−1,7,−6) respectively then the co-ordinates of CCC

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Q.Centroid of a triangle $ABC$ is at the point $(1, 1, 1)$ . If the co-ordinates of $A$ and $B$ are $(3, -5, 7)$ and $(-1, 7, -6)$ respectively then the co-ordinates of $C$

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