Question

find the length of the medians of a triangle whose vertices are A(-2,-1),B(1,0) and C(4,3)

Answer 1

Step-by-step explanation:

A(0,1), B(2,1) and C(0,3) are the vertices of Δ ABC.

AD, BE and CF are median

We have mid point formula,

P(X,Y)=(  

2

x  

1

​  

+x  

2

​  

 

​  

,  

2

y  

1

​  

+y  

2

​  

 

​  

)

∴ Coordinate of point D=(  

2

2+0

​  

,  

2

1+3

​  

)=(1,2)

∴AD=  

(1−0)  

2

+(2+1)  

2

 

​  

=  

1+9

​  

=  

10

​  

units

∴ Coordinate of point E =(  

2

0+0

​  

,  

2

−1−3

​  

)=(0,1)

∴BE=  

(0−2)  

2

+(1−1)  

2

 

​  

=  

4

​  

=2 units

∴ Coordinate of point F =(  

2

2+0

​  

,  

2

−1+1

​  

)=(1,0)

∴CF=  

(1−0)  

2

+(0−3)  

2

 

​  

=  

1+9

​  

=  

10

​  

units

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