A triangle has corners at $(2 ,3 )$ , $(1 ,-2 )$ , and $(-6 ,6 )$ . If the triangle is dilated by a factor of $5$ about point #(-3 ,2 ), how far will its centroid move?

Question

1530 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-20T13:37:33

The centroid will move by $=4/3sqrt37$

The corners of the triangle are $A=(2,3)$ , $B=(1,-2)$ and $C=(-6,6)$

The centroid of triangle $ABC$ is

$C=((2+1-6)/3, (3-2+6)/3)=(-1,7/3)$

Let the the new centroid be $C'=(x,y)$ after dilatation.

Let the fixed point be $D=(-3,2)$

Let the coefficient of dilatation be $k=5$

Therefore, in vector notation

$vec(DC')=kvec(DC)$

$((x-(-3)),(y-2))=5((-1-(-3)),(7/3-2))$

$x+3=5*2$ , $=>$ , $x=7$

$y-2=5*(1/3)$ , $=>$ , $y=11/3$

The centroid will move by

$=sqrt((7+1)^2+(11/3-7/3)^2)$

$=sqrt(64+16/9)$

$=sqrt(592/9)$

$=4/3sqrt37$

A triangle has corners at (2 ,3 )(2 ,3 ), (1 ,-2 )(1 ,-2 ), and (-6 ,6 )(-6 ,6 ). If the triangle is dilated by a factor of 5 5 about point #(-3 ,2 ), how far will its centroid move?