Question

1. The vertices of a triangle are (2,1), (-2,-2), (1,0). Then sum of squares of the
lengths of the medians of the triangle is
1. 25 2. 40
3. 30 4. 45
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Answer 1

Hope it's helpful ..... ❤

Answer 2

Given:

Vertices of triangle ABC are given,

A= (2,1)

B=(-2,-2)

C=(1,0)

To Find:

Find the sum of the squares of the medians of the triangle.

Solutions:

Let AD, BE, CF be the medians.

Point D:

x= (-2+1)/2

 =-1/2

y=(-2+0)/2

 =-1

D= (-0.5,-1)

AD²= (2+0.5)²+(1+1)²

      =2.5²+2²

      =6.25+4

      =10.25

Point E:

x=(2+1)/2

 =1.5

y=(1+0)/2

 =0.5

BE²=(-2-1.5)²+(-2-0.5)²

     =3.5²+2.5²

     =12.25+6.25

     =18.5

Point F:

x=(2-2)/2

 =0

y=(1-2)/2

 =-0.5

CF²=(1-0)²+(0+0.5)²

      =1+0.25

      =1.25

AD²+BE²+CF²=10.25+18.5+1.25

                      =30

Hence the sum of the square of the medians is 30.