Question

If A( 5,-1), B( -3,-2) and C(-1,8) are the vertices of triangle ABC, then find the length of median through A and the coordinates of the centroid.

Answer 1

Answer:

Let AD be the median through the vertex A of△ABC. Then, D is the mid-point of BC. So, the coorinates of D are(

2

−3−1

,

2

−2+8

)i.e.,(−2,3).

∴AD=

(5+2)

2

+(−1−3)

2

=

49+16

=

65

units

Let G be the centroid of △ABC. Then, G lies on median AD and divides it in the ratio 2:1. So, coordinates of G are

(

2+1

2×−2+1×5

,

2+1

2×3+1×−1

)=(

3

−4+5

,

3

6−1

)=(

3

1

,

3

5

)