A triangle has corners at #(3, 8 )#, #( 2, 1 )#, and #( 9 , 6 )#. If the triangle is dilated by # 3 x# around #(1, 2)#, what will the new coordinates of its corners be?

1 Answer
Jim G.
Oct 28, 2017

#(7,20),(4,-1)" and "(25,14)#

Explanation:

#"let the 3 corners be"#

#A=(3,8),B=(2,1)" and "C=(9,6)#

#"and "A',B',C'"be the images of "A,B" and "C#

#"let "D=(1,2)" be the centre of dilatation"#

#•color(white)(x)A=(3,8)#

#vec(DA')=3vec(DA)#

#vec(DA)=ula-uld=((3),(8))-((1),(2))=((2),(6))#

#rArrvec(DA')=3((2),(6))=((6),(18))#

#rArrA'=(1+6,2+18)=(7,20)#

#•color(white)(x)B=(2,1)#

#vec(DB')=3vec(DB)#

#vec(DB)=ulb-uld=((2),(1))-((1),(2))=((1),(-1))#

#rArrvec(DB')=3((1),(-1))=((3),(-3))#

#rArrB'=(1+3,2-3)=(4,-1)#

#•color(white)(x)C=(9,6)#

#vec(DC')=3vec(DC)#

#vec(DC)=ulc-uld=((9),(6))-((1),(2))=((8),(4))#

#rArrvec(DC')=3((8),(4))=((24),(12))#

#rArrC'=(1+24,2+12)=(25,14)#

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