A triangle as corners at $(3, 5)$ $(3 ,5 )$ , $(5, 2)$ $(5 ,2)$ , and $(9, 4)$ $(9 ,4)$ . If the triangle is dilated by a factor of $4$ $4$ about #(1 ,9), how far will its centroid move?

Question

1383 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-12T12:51:30

The centroid will move by $= 21.3$ $=21.3$

The centroid of the triangle, $A = (3, 5)$ $A=(3,5)$ , $B = (5, 2)$ $B=(5,2)$ and $C = (9, 4)$ $C=(9,4)$ is

$C_{c} = (\frac{3 + 5 + 9}{3}, \frac{5 + 2 + 4}{3})$ $C_c=((3+5+9)/3,(5+2+4)/3)$

$= (\frac{17}{3}, \frac{11}{3})$ $=(17/3,11/3)$

Let the point $D = (1, 9)$ $D=(1,9)$

Let the centroid be $C_c'$ after the dilatation

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

$=4<17/3-1,11/3-9>$

$=<56/3,-64/3>$

$C_c'=(56/3,-64/3)+(1,9)$

$=(59/3,-37/3)$

The distance between the centroids is

$d=sqrt((59/3-17/3)^2+(-37/3-11/3)^2)$

$=sqrt((42/3)^2+(48/3)^2)$

$=sqrt(14^2+16^2)$

$=sqrt452$

$=21.3$

A triangle as corners at (3 ,5 )(3,5)(3 ,5 ), (5 ,2)(5,2)(5 ,2), and (9 ,4)(9,4)(9 ,4). If the triangle is dilated by a factor of 4 44 about #(1 ,9), how far will its centroid move?