Question

find the centroid of the triangle whose vertices are A(-5,-5),B(1,-4),C(-4,-2).and verify the centroid G which divides the line segment AB internally in the ratio 2:1

Answer 1

Answer:

-4 , -11/2

Step-by-step explanation:

1. (-5+1-4)/3
2. = -4

1. (-5-4-2)/2
2. = -11/2

Therefore the

-4 , -11/2. are the cordinate of centroid of triangle

Answer 2

Given: A triangle whose vertices are A(-5,-5), B(1,-4) and C(-4,-2)

To find: 1- The centroid G

2- The centroid divides line segment AB internally in 2:1

Explanation: The vertices are (-5,-5) , (1,-4) and (-4,-2). The formula for calculating centroid is:

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

Here x1= -5, x2= 1, x3= -4 ,y1= -5, y2= -4 and y3= -2

Putting values,

(x,y) = -5+1-4/3 , -5-4-2/3

= -8/3, -11/3

The coordinates of centroid is -8/3,-11/3

Now, A(-5,-5) and B(1,-4) and G(-8/3,-11/3)

For internal division of a line segment:

mx1+nx2/m+n , my2+ny1/m+n

Here, m=2,n=1, x1=-5, x2=1, y1= -5 and y2= -4

Putting values,

(x,y) = 2*-5+1*1/2+1, 2*-5+1*-4/2+1

= -8/3, -11/3

which is the same as the centroid which proves centroid divides AB in ratio 2:1 internally

Therefore, the coordinates of centroid G are (-8/3,-11/3) and it divides AB in 2:1 internally.