A triangle has corners at #(1, 7 )#, #( 8, 3 )#, and #( 4 , 8 )#. If the triangle is dilated by # 2 x# around #(2, 5)#, what will the new coordinates of its corners be?

1 Answer
Jim G.
Feb 17, 2018

#(0,9),(14,1)" and "(6,11)#

Explanation:

#"label the vertices of the triangle"#

#A(1,7),B(8,3)" and "C(4,8)#

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

#"let the centre of dilatation be "D(2,5)#

#rArrvec(DA')=color(red)(2)vec(DA)#

#rArrula'-uld=2(ula-uld)=2ula-2uld#

#rArrula'=2ula-uld#

#color(white)(rArrula')=2((1),(7))-((2),(5))=((0),(9))#

#"the coordinates of A' are the components of "ula'#

#rArrA'=(0,9)#

#"similarly "#

#vec(DB')=color(red)(2)vec(DB)#

#rArrulb'=2ulb-uld#

#color(white)(rArrulb')=2((8),(3))-((2),(5))=((14),(1))#

#rArrB'=(14,1)#

#"and "vec(DC')=color(red)(2)vec(DC)#

#rArrulc'=2ulc-uld#

#color(white)(rArrulc')=2((4),(8))-((2),(5))=((6),(11))#

#rArrC'=(6,11)#

#color(blue)"Result after dilatation"#

#(1,7)to(0,9),(8,3)to(14,1),(4,8)to(6,11)#

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