Question

In the figure, find the coordinates of A.

​

Answer 1

$\textbf{Given:}$

$\textsf{The vertices of triangle ABC are A(x,y),B(3,-5),C(-7,4) and}$

$\textsf{centroid G(2,-1)}$

$\textbf{To find:}$

$\textsf{The co-ordinates of A}$

$\mathsf{}$

$\textbf{Solution:}$

$\textsf{Centroid of triangle ABC=(2,-1)}$

$\implies\mathsf{\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)=(2,-1)}$

$\implies\mathsf{\left(\dfrac{x+3+(-7)}{3},\dfrac{y+(-5)+4}{3}\right)=(2,-1)}$

$\implies\mathsf{\left(\dfrac{x-4}{3},\dfrac{y-1}{3}\right)=(2,-1)}$

$\implies\mathsf{\dfrac{x-4}{3}=2}$

$\implies\mathsf{x-4=6}$

$\implies\mathsf{x=6+4}$

$\implies\mathsf{x=10}$

$\mathsf{and}$

$\implies\mathsf{\dfrac{y-1}{3}=-1}$

$\implies\mathsf{y-1=-3}$

$\implies\mathsf{y=1-3}$

$\implies\mathsf{y=-2}$

$\therefore\underline{\textsf{The co-ordinates of A is (10,-2)}}$

$\textbf{Find more:}$

In a triangle ABC A=(5,8)D is the midpoint of the side BC d=(2,-1).find the centroid of triangle ABC

https://brainly.in/question/15411171