SOLUTION: Find coordinates for the centroid of the triangle whose vertices are (a) (-1,5), (-2,8) and (3,3); b) (2,7),(8,1) and (14,11); (c) (a,p), (b,q) and (c,r).

Question 149703: Find coordinates for the centroid of the triangle whose vertices are (a) (-1,5), (-2,8) and (3,3); b) (2,7),(8,1) and (14,11); (c) (a,p), (b,q) and (c,r).
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The formula for the coordinates of the centroid is

and

note: notice how we're simply averaging the coordinates

where

, and

are the coordinates of the three vertices a, b, and c respectively.

a)

Start with the formula for finding the x-coordinate of the centroid.

Plug in the x-coordinates of the given points

Add

Multiply.

So the x-coordinate of the centroid is

------

Start with the formula for finding the y-coordinate of the centroid.

Plug in the x-coordinates of the given points

Add

Simplify.

So the y-coordinate of the centroid is

So the centroid is (0,5.33)

b)

Start with the formula for finding the x-coordinate of the centroid.

Plug in the x-coordinates of the given points

Add

Multiply.

So the x-coordinate of the centroid is

------

(2,7),(8,1) and (14,11)
Start with the formula for finding the y-coordinate of the centroid.

Plug in the x-coordinates of the given points

Add

Simplify.

So the y-coordinate of the centroid is

So the centroid is (0,5.33)

c)

(a,p), (b,q) and (c,r).
Start with the formula for finding the x-coordinate of the centroid.

Plug in the x-coordinates of the given points

So the x-coordinate of the centroid is

------

Start with the formula for finding the x-coordinate of the centroid.

Plug in the x-coordinates of the given points

So the y-coordinate of the centroid is

So the centroid is (,)

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