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

1 Answer
Jim G.
Jun 5, 2017

#(2,-3),(6,1),(0,5)#

Explanation:

#"let the vertices be " A(2,1),B(4,3),C(1,5)#

#"and " A',B',C' "be the images of A,B,C respectively under"#
#"the dilatation"#
#"let the centre of dilatation be " D(2,5)#

#vec(DA)=ula-uld=((2),(1))-((2),(5))=((0),(-4))#

#rArrvec(DA')=color(red)(2)((0),(-4))=((0),(-8))#

#rArrA'=(2+0,5-8)=(2,-3)larrcolor(red)" image of A"#

#vec(DB)=ulb-uld=((4),(3))-((2),(5))=((2),(-2))#

#rArrvec(DB')=color(red)(2)((2),(-2))=((4),(-4))#

#rArrB'=(2+4,5-4)=(6,1)larrcolor(red)" image of B"#

#vec(DC)=ulc-uld=((1),(5))-((2),(5))=((-1),(0))#

#rArrvec(DC')=color(red)(2)((-1),(0))=((-2),(0))#

#rArrC'=(2-2,5-0)=(0,5)larrcolor(red)" image of C"#

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