The centroid of the triangle whose vertices a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The centroid $(G)$ of a triangle with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by the formula: $G = (\frac{x_1

Vedclass · Accepted Answer

$(\frac{4}{3}, 0, -\frac{1}{3})$

Vedclass · Answer

(B) The centroid $(G)$ of a triangle with vertices $(x_1, y_1, z_1)$,$(x_2, y_2, z_2)$,and $(x_3, y_3, z_3)$ is given by the formula: $G = (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}, \frac{z_1 + z_2 + z_3}{3})$ Given vertices are $P(1, -2, 1)$,$Q(2, 3, -1)$,and $R(1, -1, -1)$. Substituting the values: $x$-coordinate $= \frac{1 + 2 + 1}{3} = \frac{4}{3}$ $y$-coordinate $= \frac{-2 + 3 - 1}{3} = \frac{0}{3} = 0$ $z$-coordinate $= \frac{1 - 1 - 1}{3} = -\frac{1}{3}$ Thus,the centroid is $(\frac{4}{3}, 0, -\frac{1}{3})$.

The centroid of the triangle whose vertices are $P(1, -2, 1)$,$Q(2, 3, -1)$,and $R(1, -1, -1)$ is:

Similar Questions

If $A(2, 4, -1)$,$B(3, 6, -1)$,and $C(4, 5, 1)$ are three consecutive vertices of a parallelogram,then its fourth vertex is

If $G(3, -5, r)$ is the centroid of triangle $ABC$ where $A(7, -8, 1)$,$B(p, q, 5)$,and $C(q+1, 5p, 0)$ are the vertices of the triangle,then the values of $p, q, r$ are respectively . . . . . . .

If the origin is the centroid of the triangle whose vertices are $A(2, p, -3)$,$B(q, -2, 5)$,and $C(-5, 1, r)$,then

If the origin is the centroid of the triangle $PQR$ with vertices $P(2a, 2, 6)$,$Q(-4, 3b, -10)$,and $R(8, 14, 2c)$,then find the values of $a, b$,and $c$.

If $O(0,0,0), A(3,0,0), B(0,4,0)$ form a triangle,then the incentre of triangle $OAB$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module