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

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Answer 1 · 2017-03-14T09:20:31

The new coordinates are #(8,31)#, #(50,0)# and #(22,38)#

We can work this with vectors

Let the points be

#A=(2,7)#

#B=(8,3)#

#C=(4,8)#

#D=(1,3)#

#vec(DA)= <2-1,7-3> = <1,4>#

#vec(DB) = <8-1,3-3> = <7,0>#

#vec(DC)= <4-1, 8-3> = <3,5>#

Let #A'# be the new point

Then

#vec(DA')=7vec(DA)=7+<1,4> = <7,28>#

So the coordinates of #A'=(1+7,3+28)=(8,31)#

Let #B'# be another new point

Then,

#vec(DB')=7vec(DB)=7* <7,0> =<49,0>#

The coordinates of #B'=(1+49,3+0) =(50,0)#

Let #C'# be another new point

Then,

#vec(DC')=7vec(DC)=7* <3,5> =<21,35>#

The coordinates of #C'=(1+21,3+35) =(22,38)#