Question

find the centroid of a triangle whose vertices are (7,4),(1,2) and (3,8).​

Answer 1

Answer:

(11/3,14/3)

Step-by-step explanation:

centroid = (x1 + x2 + x3 /3 , y1+y2+y3/3)

centroid = 7+1+3/3, 4+2+8/3

= 11/3, 14/3

Answer 2

Answer:

Given: Coordinates of the vertices of a triangle which are (7,4), (1,2) and (3,8)

To find: Centroid of the given triangle

Step-by-step explanation:

Step 1: Centroid of a triangle is the point in a triangle where the medians of the sides of triangle coincide. It is denoted by 'G'. The formula to find the centroid is given by $G = (\frac{x_{1}+x_{2}+x_{3} }{3} ,\frac{y_{1}+y_{2}+y_{3} }{3})$

where $x_{1}, x_{2}, x_{3}$ are the $x$-coordinates of the three vertices of the triangle and $y_{1}, y_{2}, y_{3}$ are the $y$-coordinates of the vertices of triangle.

Step 2: Here, the coordinates of vertices are given as (7,4), (1,2) and (3,8) where $x_{1}=7\\ x_{2}=1\\x_{3}=3\\y_{1}=4\\y_{2}=2\\y_{3}=8$

Step 3: Substitute the given values into the formula of centroid

$\frac{x_{1}+x_{2}+x_{3} }{3}=\frac{7+1+3}{3}=\frac{11}{3}$

$\frac{y_{1}+y_{2}+y_{3} }{3}=\frac{4+2+8}{3}=\frac{14}{3}$

∴ G = $\frac{11}{3},\frac{14}{3}$

Final Answer: The centroid of triangle having vertices (7,4), (1,2) and (3,8) is $\frac{11}{3},\frac{14}{3}$