A line segment has endpoints at #(1 ,2 )# and #(3 , 1)#. The line segment is dilated by a factor of #1/4 # around #(2 , 5)#. What are the new endpoints and length of the line segment?

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Answer 1 · 2016-03-08T05:25:45

New endpoints #(7/4, 17/4)# and #(9/4, 4)#
New Length #l=sqrt5/4#

First Endpoint #(x_1, y_1)#
For #x_1:#

#(2-x_1)/(2-1)=1/4#

#x_1=7/4#

For #y_1:#

#(5-y_1)/(5-2)=1/4#

#y_1=17/4#

#(7/4, 17/4)#

Second Endpoint #(x_2, y_2)#

For #x_2:#

#(2-x_2)/(2-3)=1/4#

#x_2=9/4#

For #y_2:#

#(5-y_2)/(5-1)=1/4#

#y_2=4#

#(9/4, 4)#

Length #l=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#l=sqrt((9/4-7/4)^2+(4-17/4)^2)#

#l=sqrt((2/4)^2+(-1/4)^2)#

#l=sqrt5/4#

God bless... I hope the explanation is useful