Let A(2, -3) and B(-2, 1) be vertices of a tr | vedclass

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

Question

(D) Let the third vertex $C$ be $(x, y)$.The centroid $G$ of triangle $ABC$ is given by:$G = \left( \frac{2 - 2 + x}{3}, \frac{-3 + 1 + y}{3} \right)

Vedclass · Accepted Answer

$2x + 3y = 9$

Vedclass · Answer

(D) Let the third vertex $C$ be $(x, y)$.The centroid $G$ of triangle $ABC$ is given by:$G = \left( \frac{2 - 2 + x}{3}, \frac{-3 + 1 + y}{3} \right) = \left( \frac{x}{3}, \frac{y - 2}{3} \right)$.Given that the centroid moves on the line $2x + 3y = 1$,we substitute the coordinates of $G$ into this equation:$2\left( \frac{x}{3} \right) + 3\left( \frac{y - 2}{3} \right) = 1$.Multiplying the entire equation by $3$,we get:$2x + 3(y - 2) = 3$$2x + 3y - 6 = 3$$2x + 3y = 9$.Thus,the locus of vertex $C$ is $2x + 3y = 9$.

Let $A(2, -3)$ and $B(-2, 1)$ be vertices of a triangle $ABC$. If the centroid of this triangle moves on the line $2x + 3y = 1$,then the locus of the vertex $C$ is the line

Similar Questions

If the distance from a variable point $P$ to the point $(4, 3)$ is equal to the perpendicular distance from $P$ to the line $x + 2y - 1 = 0$,then the equation of the locus of the point $P$ is

If non-zero numbers $a, b, c$ are in harmonic progression,then the straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ always passes through a fixed point. Find the coordinates of that point.

The locus of points $(x, y)$ in the plane satisfying $\sin ^2 x + \sin ^2 y = 1$ consists of

$A$ point moves in the $XY$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $3$. The area enclosed by the locus of that point is (in sq. units)

$A$ variable line passes through a fixed point $(x_{1}, y_{1})$ and meets the axes at $A$ and $B$. If the rectangle $OAPB$ is completed, the locus of $P$ is, ($O$ being the origin of the system of axes).

Vedclass Test Series

Exam Paper Generator

Online Exam Module