Math, asked by Alran1406, 4 months ago

Two vertices of a triangle are (4,-5) and (-5,-2). If the centroid of the triangle
is the origin, determine the third vertex of the triangle.​

Answers

Answered by MaheswariS
1

\textbf{Given:}

\textsf{Two vertices of triangle are (4,-5) and (-5,-2)}

\textsf{Centroid of the triangle is (0,0)}

\textbf{To find:}

\textsf{Third vertex of the triangle}

\textbf{Solution:}

\textsf{Since centroid of the triangle is (0,0), we have}

\mathsf{\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)=(0,0)}

\mathsf{\left(\dfrac{4+(-5)+x_3}{3},\dfrac{(-5)+(-2)+y_3}{3}\right)=(0,0)}

\mathsf{\left(\dfrac{-1+x_3}{3},\dfrac{-7+y_3}{3}\right)=(0,0)}

\implies\mathsf{\dfrac{-1+x_3}{3}=0\implies\,-1+x_3=0\,\implies\,x_3=1}

\mathsf{and}

\mathsf{\dfrac{-7+y_3}{3}=0\implies\,-7+y_3=0\,\implies\,y_3=7}

'

\therefore\boxed{\textsf{Third vertex is (1,7)}}

\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

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