A line segment has endpoints at #(9 ,2 )# and #(7 , 4)#. The line segment is dilated by a factor of #4 # around #(1 , 5)#. What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jul 14, 2018

#color(orange)("New coordinates are " (33,-7), (-25, 1)#

#color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137#

Explanation:

#A(8,4), B(9,2), " about point " D (1,5), " dilation factor "4#

#A'((x),(y)) =(4)a - (3)d =(4)*((9),(2)) - (3)*((1),(5)) = ((33),(-7))#

#B'((x),(y)) = (4)b - (3)d = (4)*((7),(4)) - (3)*((1),(5)) = ((25),(1))#

#color(orange)("New coordinates are " (33,-7), (-25, 1)#

#color(orange)("Length of the line segment '" = sqrt((33-25)^2 + (-7-1)^2) ~~ 11.3137#

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