Find the third vertex of a triangle whose cen | vedclass

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

Question

(A) Let the third vertex of the triangle be $A(x, y, z)$.The given vertices are $B(2, 4, 6)$ and $C(0, -2, -5)$.The centroid $G$ of a triangle with ve

Vedclass · Accepted Answer

$(-2, -2, -1)$

Vedclass · Answer

(A) Let the third vertex of the triangle be $A(x, y, z)$.The given vertices are $B(2, 4, 6)$ and $C(0, -2, -5)$.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 $G = \left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}, \frac{z_1+z_2+z_3}{3}\right)$.Given that the centroid is the origin $(0, 0, 0)$,we have:$(0, 0, 0) = \left(\frac{2+0+x}{3}, \frac{4-2+y}{3}, \frac{6-5+z}{3}\right)$.Equating the coordinates:$\frac{2+x}{3} = 0 \implies x = -2$.$\frac{2+y}{3} = 0 \implies y = -2$.$\frac{1+z}{3} = 0 \implies z = -1$.Thus,the third vertex is $(-2, -2, -1)$.

Find the third vertex of a triangle whose centroid is the origin and two vertices are $(2, 4, 6)$ and $(0, -2, -5)$.

Similar Questions

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

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 $C$.

If $A(-4, 5, p)$,$B(3, 1, 4)$,and $C(-2, 0, q)$ are the vertices of a triangle $ABC$ and $G(r, q, 1)$ is its centroid,then the value of $2p + q - r$ is equal to

If two vertices of a triangle are $A(3,1,4)$ and $B(-4,5,-3)$ and the centroid of the triangle is $G(-1,2,1)$,then the third vertex $C$ of the triangle is

Let $ABCD$ be a parallelogram and $E$ be the mid-point of $AB$. If $P$ is the point of intersection of $DE$ and $AC$,then $\frac{DP}{PE} + \frac{AP}{PC} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module