The centroid of a variable triangle ABC is at | vedclass

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

Question

(C) Let the coordinates of $C$ be $(h, k)$.The centroid $G$ of triangle $ABC$ is given by $\left( \frac{2+3+h}{3}, \frac{3+2+k}{3} \right) = \left( \f

Vedclass · Accepted Answer

a circle of diameter $30$ units

Vedclass · Answer

(C) Let the coordinates of $C$ be $(h, k)$.The centroid $G$ of triangle $ABC$ is given by $\left( \frac{2+3+h}{3}, \frac{3+2+k}{3} ight) = \left( \frac{5+h}{3}, \frac{5+k}{3} ight)$.Given that the distance of the centroid from the origin is $5$ units,we have $\sqrt{\left( \frac{5+h}{3} ight)^2 + \left( \frac{5+k}{3} ight)^2} = 5$.Squaring both sides,we get $\left( \frac{5+h}{3} ight)^2 + \left( \frac{5+k}{3} ight)^2 = 25$.Multiplying by $9$,we get $(h+5)^2 + (k+5)^2 = 225$.Replacing $(h, k)$ with $(x, y)$,the locus of $C$ is $(x+5)^2 + (y+5)^2 = 15^2$.This represents a circle with radius $r = 15$ units.The diameter of the circle is $2r = 2 	imes 15 = 30$ units.

The centroid of a variable triangle $ABC$ is at a distance of $5$ units from the origin. If $A = (2, 3)$ and $B = (3, 2)$,then the locus of $C$ is

Similar Questions

The locus of the centre of the circle touching the $x$-axis and passing through the point $(-1, 1)$ is

If the sum of the distances of a point from the origin and the line $x = 2$ is $4$,then its locus is

The locus of the moving point $P$,such that $2PA = 3PB$ where $A$ is $(0,0)$ and $B$ is $(4,-3)$,is

Let $S$ be the set of points on the $X$-axis lying at a distance of $d$ units from $(3, 4)$. Which of the following is true?

The locus of the centre of a circle touching both the coordinate axes is

Vedclass Test Series

Exam Paper Generator

Online Exam Module