A triangle has corners at #(4, 5 )#, #( 2, 3 )#, and #(2 , 2 )#. If the triangle is dilated by # 4 x# around #(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)#