If A(2, -3) and B(-2, 1) are two vertices of | vedclass

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(B) Let the third vertex be $C = (h, k)$.Given vertices are $A = (2, -3)$ and $B = (-2, 1)$.The centroid $G$ of $	riangle ABC$ is given by the formul

Vedclass · Accepted Answer

$2x + 3y = 9$

Vedclass · Answer

(B) Let the third vertex be $C = (h, k)$.Given vertices are $A = (2, -3)$ and $B = (-2, 1)$.The centroid $G$ of $	riangle ABC$ is given by the formula $G = \left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}ight)$.Substituting the values,$G = \left(\frac{2 - 2 + h}{3}, \frac{-3 + 1 + k}{3}ight) = \left(\frac{h}{3}, \frac{k - 2}{3}ight)$.Since the centroid $G$ lies on the line $2x + 3y = 1$,we substitute the coordinates of $G$ into the line equation:$2\left(\frac{h}{3}ight) + 3\left(\frac{k - 2}{3}ight) = 1$.Multiplying the entire equation by $3$,we get $2h + 3(k - 2) = 3$.$2h + 3k - 6 = 3$.$2h + 3k = 9$.Replacing $(h, k)$ with $(x, y)$,the locus of vertex $C$ is $2x + 3y = 9$.Thus,option $B$ is correct.

If $A(2, -3)$ and $B(-2, 1)$ are two vertices of a $\triangle ABC$ and if the centroid of $\triangle ABC$ lies on the line $2x + 3y = 1$,then the locus of vertex $C$ of $\triangle ABC$ is equal to

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