A line segment has endpoints at #(9 ,7 )# and #(5 ,4 )#. The line segment is dilated by a factor of #3 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?

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Answer 1 · 2018-02-10T09:17:40

New end points #A'((5),(4)), B' ((1),(1))#

Length of line segment #vec(A'B') = color(green)(5)#

Given #A ((9),(7)), B ((5),(4)), C ((4),(3))# & dilation factor 3

#vec(A'C) = 4 * vec(AC)#

#A' ((x-4),(y-3)) = 3 * ((9-4),(7-3))=> ((5),(4))#

#A' ((9),(7))#

#vec(B'C) = 4 * vec(BC)#

#B' ((x-4),(y-3)) = 3 * ((5-4),4-3))=> ((1),(1))#

#B' ((5),(4))#

Length of line segment #vec(A'B') = sqrt((5-1)^2 + (4-1)^2) = color(green)(5)#