A triangle has corners at (1,9), (5,7), and (3,8). How far is the triangle's centroid from the origin?

2 Answers
Jan 10, 2018

73 units

Explanation:

If,
(x1,y1)(1,9)
(x2,y2)(5,7)
(x3,y3)(3,8)
are the vertices of a triangle then,

Centroid (G) of a triangle is given by,
G=(x1+x2+x33,y1+y2+y33)

So, substituting the above values we get,
G=(3,8)

Now, to find distance 'd' between (0,0) and (3,8) use distance formula

d=(80)2+(30)2

d=73 units

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Jan 10, 2018

Distance of centroid from origin is 8.544

Explanation:

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Formula to get centroid of a triangle, given the coordinates of three vertices is

G(x,y)=x1+x2+x33,y1+y2+y33

Gx=1+5+33=3

Gy=9+7+83=8

Coordinates of centroid G(x,y)=(3,8)

Coordinates of origin O(x,y)=(0.0)

Distance of centroid from origin is
d=(30)2+(80)2=32+82=8.544