Find the centroid of a triangle,the mid-point | vedclass

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

Question

(A) Let the vertices of the triangle be $A(x_1, y_1, z_1)$,$B(x_2, y_2, z_2)$,and $C(x_3, y_3, z_3)$.The mid-points of the sides are given as $D(1, 2,

Vedclass · Accepted Answer

$G(1, 1, -2)$

Vedclass · Answer

(A) Let the vertices of the triangle be $A(x_1, y_1, z_1)$,$B(x_2, y_2, z_2)$,and $C(x_3, y_3, z_3)$.The mid-points of the sides are given as $D(1, 2, -3)$,$E(3, 0, 1)$,and $F(-1, 1, -4)$.We know that the centroid of the triangle formed by the mid-points of the sides of a triangle is the same as the centroid of the original triangle.The centroid $G(x, y, z)$ of $\Delta DEF$ is calculated as:$x = \frac{1 + 3 + (-1)}{3} = \frac{3}{3} = 1$$y = \frac{2 + 0 + 1}{3} = \frac{3}{3} = 1$$z = \frac{-3 + 1 + (-4)}{3} = \frac{-6}{3} = -2$Therefore,the centroid of the triangle is $G(1, 1, -2)$.

Find the centroid of a triangle,the mid-points of whose sides are $D(1, 2, -3)$,$E(3, 0, 1)$,and $F(-1, 1, -4)$.

Similar Questions

The triangle formed by the points $(0, 7, 10), (-1, 6, 6), (-4, 9, 6)$ is

If the points $(-1, 3, 2)$,$(-4, 2, -2)$,and $(5, 5, \lambda)$ are collinear,then $\lambda = $

Given $\triangle ABC$ such that $A = 2\hat{i} - \hat{j} + \hat{k}$,$B = \hat{i} - 3\hat{j} - 5\hat{k}$,and $C = 3\hat{i} - 4\hat{j} - 4\hat{k}$,then $\triangle ABC$ is:

If a triangle $ABC$ with two vertices $A(5,4,6)$ and $B(1,-1,3)$ has its centroid at $\left(\frac{10}{3}, 2, \frac{11}{3}\right)$, then the third vertex $C$ is

Verify that the points $(0, 7, -10)$,$(1, 6, -6)$,and $(4, 9, -6)$ are the vertices of an isosceles triangle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module