Question

Centroid of triangle vertices are (-4,4),(-2,2),(-6,6)

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore Coordinate\:of\:G=(-4,4)}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies Coordinate \: of \: A= ( - 4,4) \\ \\ \implies Coordinate \: of \: B = ( - 2,2) \\ \\ \implies Coordinate \: of \: C = (- 6,6) \\ \\ \underline \bold{To \: Find : } \\ \implies Coordinate \: of \: G = ?$

• According to given question :

$\bold{Using \: centroid \: formula : } \\ \\ \bold{For \: x : } \\ \implies x = \frac{ x_{ 1 } +x_{ 2 } +x_{ 3 } }{3} \\ \\ \implies x = \frac{ - 4 - 2 - 6}{3} \\ \\ \implies x = \frac{ \cancel{- 12}}{ \cancel3} \\ \\ \bold{ \implies x = - 4} \\ \\ \bold{for \:y : } \\ \implies y = \frac{y_{ 1 } + y_{ 2 } + y_{ 3}}{3} \\ \\ \implies y = \frac{4 + 2 + 6}{3} \\ \\ \implies y = \frac{\cancel{12}}{\cancel3} \\ \\ \bold{\implies y = 4}$

Answer 2

Answer:

Centroid Coordinates are (-4,4)

Step-by-step explanation:

Let A(-4,4) , B(-2,2) and (-6,6) be three vertices of the given ΔABC and (x,y) be the co-ordinates of the centroid of the triangle.

Now, by centroid formula, (x,y) = {$\frac{x1 + x2 + x3}{3}$, $\frac{y1+ y2+ y3}{3}$}

so, on putting this formula, we get

x = $\frac{ -4 -2 -6}{3}$

and y = $\frac{4+ 2 + 6}{3}$

or, x = $\frac{-12}{3}$ = -4

and y= $\frac{12}{3}$ = 4

So, centroid coordinates of the triangle are (-4,4)