Question

If a(-2,4) , b(0,0) , c(14,2) are the vertices of ∆abc then coordinates of centroid of ∆abc are

Answer 1

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

$\green{\bold{\therefore{\text{Centroid\:G=(4,2)}}}}$

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

$\green {\underline{\bold{Given : }}} \\ \implies \text{Coordinate \: of \: a \: (-2,4)} \\ \\ \implies \text{Coordinate \: of \: b\: (0,0)} \\ \\ \implies \text{Coordinate \: of \: c \: (14,2)} \\ \\ \red {\underline{\bold{to \: find : }}} \\ \implies \text{coordinate \: of \: G \: =?}$

• According to given question :

• Consider abc a triangle with vertices and their coordinates are given.

• Take centroid as G.

• whose coordinates are (x,y)

$\text{Using \: centroid \: formula \: of \: triangle } \\ \implies x = \frac{ x_{1} +x_{2} +x_{3} }{3} \\ \\ \implies x = \frac{ - 2 + 0 + 14}{3} \\ \\ \implies x = \frac{12}{3} \\ \\ \green{\implies x = 4} \\ \\ \text{Similarly \: for \: ordinate \: y} \\ \implies y = \frac{ y_{1} +y_{2} +y_{3} }{3} \\ \\ \implies y = \frac{4 + 0 + 2}{3} \\ \\ \implies y = \frac{6}{3} \\ \\ \green{\implies y = 2} \\ \\ \green{\therefore \text{Centroid \: of \: triangle \: G \: (4,2)}}$

Answer 2

Answer:

Centroid G = (4,2)

Step - by - step explanation

》x = (x1 + x2 + x3)/3

》x = (-2 + 0 + 14)/3

》x = 4

For y-ordinate -

》y = (y1 + y2 + y3)/3

》y = (4 + 0 + 2)/ 3

》y = 2

@ Therefore Centroid G = (4, 2)