A triangle has corners at #(3, 4 )#, #( 6, 3 )#, and #( 7 , 2 )#. If the triangle is dilated by # 5 x# around #(1, 1)#, what will the new coordinates of its corners be?

1 Answer
Jim G.
Nov 25, 2017

#(11,16),(26,11)" and "((31,6)#

Explanation:

#"let the points be A, B and C and their images A', B' and C'"#

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

#vec(DA')=color(red)(5)vec(DA)=5(ula-uld)#

#=5[((3),(4))-((1),(1))]=5((2),(3))=((10),(15))#

#rArrA'=(1+10,1+15)=(11,16)#

#vec(DB')=color(red)(5)vec(DB)=5(ulb-uld)#

#=5[((6),(3))-((1),(1))]=5((5),(2))=((25),(10))#

#rArrB'=(1+25,1+10)=(26,11)#

#vec(DC')=color(red)(5)vec(DC)=5(ulc-uld)#

#=5[((7),(2))-((1),(1))]=5((6),(1))=((30),(5))#

#rArrC'=(30+1,5+1)=(31,6)#

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