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

1 Answer
CW
Oct 11, 2016

#(2,5),(10,1),(2,9)#

Explanation:

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#ABC# is the original triangle. #AB'C'# is the dilated triangle.

Given: #A(2,5), B(6,3), C(2,7)#

1) Given the 2X dilation is around Pt #A(2,5), A's# coordinates remain unchanged at #(2,5) #

2) From Pt #A(2,5)# to Pt #B(6,3)#
#Delta x = x_2-x_1=6-2=4#
#Delta y=y_2-y_1=3-5=-2#
Given scaling factor #=2X, => AB'=2AB#
#=> 2Deltax=2*4=8#,
#=>2Deltay=2*(-2)=-4#

#=># coordinates of #B'=(2+8, 5-4)=(10,1)#

3) From Pt #A(2,5)# to Pt #C(2,7)#
#Delta x = x_2-x_1=2-2=0# (vertical line)
#Delta y=y_2-y_1=7-5=2#
Given scaling factor #=2X, => AC'=2AC#
#=> 2Deltax=2*0=0#,
#=>2Deltay=2*2=4#

#=># coordinates of #C'=(2+0, 5+4)=(2,9)#

Hence, the new coordinates of the dilated triangle will be:
#A(2,5), B'(10,1), C'(2,9)#

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