Question

the ends of triangle are (4,6),(2,-2)and (0,2).the co-ordinate of its centroid is

Answer 1

Hi...☺

Here is your answer...✌

GIVEN THAT,

Co-ordinate of Vertices of Triangle are
(4,6) , (2,-2) , (0,2)

We know that

Co-ordinate of Centroid of triangle whose vertices are (x1 , y1) , (x2 , y2) , (x3 , y3) is

$( \: { \frac{x1 + x2 + x3}{3} , \frac{y 1+y2 + y3 }{3} } \: )$

Therefore,

Co-ordinate of Centroid of given Triangle

$= ( \: \frac{4 + 2 + 0}{3} , \frac{6 - 2 + 2}{3} \: ) \\ \\ = ( \: \frac{6}{3} , \frac{6}{3} \: ) \\ \\ = (2,2)$

HENCE,

The Co-ordinate of Centroid of given triangle is (2,2)

Answer 2

$\huge\rm\underline\pink{SOLUTION:}$

The vertices of triangle are (4,6) , (2,-2) , (0,2)

$\large\rm\bold{\boxed{G\:=\:(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})}}$

$\large\rm{G\rightarrow{Centroid\:of\:Triangle}}$

$\large\rm{x_1,x_2,x_3\rightarrow{X-coordinates\:of\:vertices}}$

$\large\rm{y_1,y_2,y_3\rightarrow{Y-coordinates\:of\:vertices}}$

$\large\rm{\implies{G\:=\:(\frac{4+2+0}{3},\frac{6-2+2}{3})}}$

$\large\rm{\implies{G\:=\:(\frac{6}{3},\frac{6}{3})}}$

$\large\rm{\implies{G\:=\:(2,2)}}$

$\large\rm{\therefore{Centroid(G)\:=\:(2,2)}}$