A triangle has corners at $(- 2, 6)$ $(-2 ,6 )$ , $(4, - 3)$ $(4 ,-3 )$ , and $(2, 9)$ $(2 ,9 )$ . If the triangle is dilated by a factor of $5$ $5$ about point #(-5 ,6 ), how far will its centroid move?

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Answer 1 · 2017-06-20T19:51:35

The centroid will move by $= 26.6$ $=26.6$

The centroid of the triangle, $A = (- 2, 6)$ $A=(-2,6)$ , $B = (4, - 3)$ $B=(4,-3)$ and $C = (2, 9)$ $C=(2,9)$ is

$C_{c} = (\frac{- 2 + 4 + 2}{3}, \frac{6 - 3 + 9}{3})$ $C_c=((-2+4+2)/3,(6-3+9)/3)$

$= (\frac{4}{3}, 4)$ $=(4/3,4)$

Let the point $D = (- 5, 6)$ $D=(-5,6)$

Let the centroid be $C_c'$ after the dilatation

$vec(DC_c')=4vec(DC_c)$

$=5<4/3+5,4-6>$

$=<95/3,-10>$

$C_c'=(95/3,-10)+(-5,6)$

$=(80/3,-4)$

The distance between the centroids is

$d=sqrt((80/3-4/3)^2+(-4-4)^2)$

$=sqrt((76/3)^2+(8)^2)$

$=sqrt(705.8)$

$=26.6$

A triangle has corners at (-2 ,6 )(−2,6)(-2 ,6 ), (4 ,-3 )(4,−3)(4 ,-3 ), and (2 ,9 )(2,9)(2 ,9 ). If the triangle is dilated by a factor of 5 55 about point #(-5 ,6 ), how far will its centroid move?