A line segment has endpoints at #(1 ,2 )# and #(3 , 9)#. The line segment is dilated by a factor of #1/2 # around #(4 , 2)#. What are the new endpoints and length of the line segment? Geometry Transformations Dilations or Scaling around a Point 1 Answer sankarankalyanam Jul 14, 2018 #color(red)("New end points are " (5/2, 2), (7/2,11/2)# #color(red)("Length of the line segment '" = sqrt((5/2- 7/2)^2 + (11/2-2)^2) ~~ 3.64# Explanation: #A(1,2), B(3,9), " about point " D (4,2), " dilation factor " 1/2# #A'((x),(y)) =(1/2)a - (-1/2)d =(1/2)* ((1),(2)) - (-1/2)*((4),(2)) = ((5/2),(2))# #B'((x),(y)) = (1/2)b - (-1/2)d = (1/2)* ((3),(9)) - (-1/2)*((4),(2)) = ((7/2),(11/2)# #color(red)("New end points are " (5/2, 2), (7/2,11/2)# #color(red)("Length of the line segment '" = sqrt((5/2- 7/2)^2 + (11/2-2)^2) ~~ 3.64# Answer link Related questions If the coordinates of a triangle are #(2,2), (2,4)#, and #(5,2)#, what are the new coordinates... What type of dilation is determined by a scale factor of 2/3? Are dilated triangles basically just similar triangles? How do you locate the center of a dilation? What are the coordinates of the image of the point #(–3, 6)# after a dilation with a center of... Is a dilation always an isometry? How do you find scale factor? How can dilations be used in real life? How do dilations relate to similarity? How do you calculate the scale factor of a dilation? See all questions in Dilations or Scaling around a Point Impact of this question 1813 views around the world You can reuse this answer Creative Commons License