A triangle has corners at (1 ,9 )(1,9), (5 ,4 )(5,4), and (6 ,2 )(6,2). How far is the triangle's centroid from the origin?

1 Answer
CW
May 5, 2018

sqrt41√41 units

Explanation:

A triangle with vertices at (x_1,y_1), (x_2,y_2) and (x_3,y_3)(x1,y1),(x2,y2)and(x3,y3) has centroid at ((x_1+x_2+x_3)/3, (y_1+y_2+y_3)/3)(x1+x2+x33,y1+y2+y33)
=>⇒ centroid of the triangle =((1+5+6)/3, (9+4+2)/3)=(4,5)=(1+5+63,9+4+23)=(4,5)
Let dd be the distance between the centroid and the origin O(0,0)O(0,0),
=> d=sqrt(4^2+5^2)=sqrt(16+25)=sqrt41⇒d=√42+52=√16+25=√41 units

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