A line segment has endpoints at (3 ,5 ) and (6 ,1 ). The line segment is dilated by a factor of 4 around (1 ,3 ). What are the new endpoints and length of the line segment?

1 Answer
Jun 19, 2018

color(indigo)(bar(A'B') = sqrt((9-21)^2 + (11+5)^2) = 20

Explanation:

A (3,5), B (6,1), C (1,3), " dilation factor " 4

A'C = 4 (a - c), A' - c = 4a - 3c

A'((x),(y)) = 4((3),(5)) - 3((1),(3)) = ((9),(11))

B'C = 4 (b - c), B' - c = 4b - 3c

B'((x),(y)) = 4((6),(1)) - 3((1),(3)) = ((21),(-5))

Length of the line segment

color(indigo)(bar(A'B') = sqrt((9-21)^2 + (11+5)^2) = 20