Question

A( 4, 2), B(-2, -6) and C(l, 1) are the vertices of triangle ABC. Find its centroid and the length of the median through C. 

Answer 1

Let G (a,b) be at centroid of Δ ABC ,

Coordinates of G are ,

G (a , b) = G = `((4 - 2 +1)/3 , (2 - 6 + 1)/3)` = G (1 , -1)

Let CE be the median through C 

∴ AE : EB = 1 : 1

Coordinates of E are

E (x , y) = E `((4 - 2)/2 , (2 - 6)/2)` = E (1 , -2)

Length of median CE = `sqrt ((1 - 1)^2 + (2 - 1)^2)`

`= sqrt 9`

= 3 units