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प्रश्न
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.
उत्तर
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
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