The centroid of a triangle ABC is at the point (1,1,1). If the coordinates of A and B are (3, -5,7) and (-1,7, -6), respectively, find the coordinates of the point C.

Question

The centroid of a triangle ABC is at the point (1,1,1). If the coordinates of A and B are (3, -5,7) and (-1,7, -6), respectively, find the coordinates of the point C. (A) (2,1,1) (B) (1,2,1) (C) (1,1,2) (D) (1,2,2)

Tardigrade Admin · Accepted Answer

Let the coordinates of C be (x,y, z). Coordinates of the centroid G = (1,1,1). Then (x+3-1/3) = 1, (y-5+7/3)=1, (z+7-6/3)=1 ⇒ x = 1, y = 1, z = 2. Hence, coordinates of C are (1,1,2).

Q. The centroid of a triangle $A BC$ is at the point $(1, 1, 1)$ . If the coordinates of $A$ and $B$ are $(3, - 5, 7)$ and $(- 1, 7, - 6)$ , respectively, find the coordinates of the point $C$ .

$(2, 1, 1)$

$(1, 2, 1)$

$(1, 1, 2)$

$(1, 2, 2)$

Let the coordinates of $C$ be $(x, y, z)$ . Coordinates of the centroid $G = (1, 1, 1)$ . Then
$\frac{x + 3 - 1}{3} = 1$ ,
$\frac{y - 5 + 7}{3} = 1$ ,
$\frac{z + 7 - 6}{3} = 1$
$\Rightarrow x = 1$ , $y = 1$ , $z = 2$ .
Hence, coordinates of $C$ are $(1, 1, 2)$ .

Q. The centroid of a triangle ABC is at the point (1,1,1). If the coordinates of A and B are (3,−5,7) and (−1,7,−6), respectively, find the coordinates of the point C.

(2,1,1)

(1,2,1)

(1,1,2)

(1,2,2)