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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.
Solution
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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From the figure given alongside, find the length of the median AD of triangle ABC. Complete the activity.
Solution:
Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.
Using midpoint formula,
x = `(5 + 3)/2`
∴ x = `square`
y = `(-3 + 5)/2`
∴ y = `square`
Using distance formula,
∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`
∴ AD = `sqrt((square)^2 + (0)^2`
∴ AD = `sqrt(square)`
∴ The length of median AD = `square`
