A triangle has corners at $(7, 2)$ $(7 ,2 )$ , $(4, 3)$ $(4 ,3 )$ , and $(5, 1)$ $(5 ,1 )$ . How far is the triangle's centroid from the origin?

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Answer 1 · 2017-12-04T19:33:58

$5.70 u n i t s$ $5.70units$

Find the centroid of the triangle

For Co-ordinates $(X 1, Y 1), (X 2, Y 2), (X 3, Y 3)$ $(X1,Y1),(X2,Y2),(X3,Y3)$

Use formula $c e n t r o i d (x, y) = (\frac{X 1 + X 2 + X 3}{3}, \frac{Y 1, Y 2, Y 3}{3})$ $centroid(x,y)=((X1+X2+X3)/3,(Y1,Y2,Y3)/3)$

Therefore substitute the Co-ordinates and the centroid Co-ordinate would be $(\frac{16}{3}, 2)$ $(16/3,2)$

Find distance from origin to the centroid by using pythagoras:

$D i s tan c e = \sqrt{{(\frac{16}{3})}^{2} + 2^{2}}$ $Distance = sqrt((16/3)^2+2^2)$

$D i s tan c e = 5.70 u n i t s$ $Distance=5.70units$

A triangle has corners at (7,2)(7 ,2 ), (4,3)(4 ,3 ), and (5,1)(5 ,1 ). How far is the triangle's centroid from the origin?