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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