Question

Find the centroid of ABC if
A = (2, 2), B = (-1,0), and C = (8,4).
([?], [ ])

Answer 1

The centroid of ABC is (3 , 2).

Explanation:

The steps are :

`centre = ( (x1 + x2 + x3)/(3) \: , \: (y1 + y2 + y3)/(3) )`

`centre = ( (2 + ( - 1) + 8)/(3) \: , \: (2 + 0 + 4)/(3) )`

`centre = ( (9)/(3) \: , \: (6)/(3) )`

`centre = (3 \: , \: 2)`

Answer 2

The centroid of ∆ABC is (3 , 2).

Step-by-step explanation:

Solution :

Here's the required formula to find the centroid of ∆ABC :

`{\star{\footnotesize{\purple{\underline{ \boxed{\sf{\pink{Centroid = \bigg( (x_1 + x_2 + x_3)/(3) \: , \: (y_1 + y_2 + y_3)/(3) \bigg)}}}}}}}}`

Where :

• 
  `\rightarrow\rm{x_1}` = 2
• 
  `\rightarrow\rm{x_2}` = -1
• 
  `\rightarrow\rm{x_3}` = 8
• 
  `\rightarrow\rm{y_1}` = 2
• 
  `\rightarrow\rm{y_2}` = 0
• 
  `\rightarrow\rm{y_3}` = 4

Substituting all the given values in the formula to find the centroid of ∆ABC

`{\implies{\small{\sf{Centroid = \bigg( (x_1 + x_2 + x_3)/(3) \: , \: (y_1 + y_2 + y_3)/(3) \bigg)}}}}`

`{\implies{\small{\sf{Centroid = \bigg( (2 + ( - 1) + 8)/(3) \: , \: (2 +0 + 4)/(3) \bigg)}}}}`

`{\implies{\small{\sf{Centroid = \bigg( (2 - 1 + 8)/(3) \: , \: (2 +0 + 4)/(3) \bigg)}}}}`

`{\implies{\small{\sf{Centroid = \bigg( (10 - 1)/(3) \: , \: (2 + 4)/(3) \bigg)}}}}`

`{\implies{\small{\sf{Centroid = \bigg( (9)/(3) \: , \: (6)/(3) \bigg)}}}}`

`{\implies{\small{\sf{Centroid = \bigg( \cancel(9)/(3) \: , \: \cancel(6)/(3) \bigg)}}}}`

`{\implies{\small{\sf{Centroid = \Big( 3\: , \: 2 \Big)}}}}`

`\star{\underline{\boxed{\rm{\red{Centroid = \Big( 3\: , \: 2 \Big)}}}}}`

Hence, the centroid of ∆ABC is (3 , 2).

`\rule{300}{1.5}`