A line segment has endpoints at #(1 ,6 )# and #(6 ,7 )#. The line segment is dilated by a factor of #4 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?

1 Answer
Dean R.
May 3, 2018

#(1,6) to (-8,15)#

#(6,7) to (12, 19) #

#l = 4 sqrt{26}#

Explanation:

I did the general case [here.](https://socratic.org/questions/a-line-segment-has-endpoints-at-2-4-and-5-3-the-line-segment-is-dilated-by-a-fac-1#604871)

#(p,q)=(4,3), quad r=4, quad (a,b)=(1,6), quad (c,d)=(6,7)#

#(a,b) to ( (1-r)p + ra, (1-r)q+ rb) #

#(1,6) to (-3(4)+4(1), -3(3) + 4(6)) = (-8,15)#

#(c,d) to ((1-r)p + rc, (1-r)q+ rd) #

#(6,7) to ( -3(4) + 4(6), -3(3) + 4(7)) = (12, 19) #

new length # l = r \sqrt{ (a-c)^2 + (b-d)^2 }#

#l = 4 \sqrt{(6-1)^2 + (7-6)^2} = 4 sqrt{26}#

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