A triangle has corners at $(4, 5)$ $(4, 5 )$ , $(2, 3)$ $( 2, 3 )$ , and $(2, 2)$ $(2 , 2 )$ . If the triangle is dilated by $4 x$ $4 x$ around $(0, 1)$ $(0, 1)$ , what will the new coordinates of its corners be?

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Answer 1 · 2018-05-31T17:38:39

$color(blue)(A'=(16x,16x+1)$

$color(blue)(B'=(8x,8x+1)$

$color(blue)(C'=(8x,4x+1)$

Let $A=(4,5) , B=(2,3), C=(2,2)$

Let:

$vec(OD)=((0),(1))$ be the position vector of the dilation point.

Let:

$vec(DA)=((4),(4))$ , $vec(DB)=((2),(2))$ , $vec(DC)=((2),(1))$

Scale factor $4x$

Then the position vectors of the images of A,B and C are:

$vec(OA')=vec(OD)+4xvec(DA)=((0),(1))+4x((4),(4))=((16x),(16x+1))$

$vec(OB')=vec(OD)+4xvec(DB)=((0),(1))+4x((2),(2))=((8x),(8x+1))$

$vec(OC')=vec(OD)+4xvec(DC)=((0),(1))+4x((2),(1))=((8x),(4x+1))$

$color(blue)(A'=(16x,16x+1)$

$color(blue)(B'=(8x,8x+1)$

$color(blue)(C'=(8x,4x+1)$

A triangle has corners at (4, 5 )(4,5)(4, 5 ), ( 2, 3 )(2,3)( 2, 3 ), and (2 , 2 )(2,2)(2 , 2 ). If the triangle is dilated by 4 x4x 4 x around (0, 1)(0,1)(0, 1), what will the new coordinates of its corners be?