A line segment has endpoints at $(1, 4)$ $(1 ,4 )$ and $(7, 9)$ $(7 ,9 )$ . The line segment is dilated by a factor of $3$ $3$ around $(2, 6)$ $(2 ,6 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-19T04:40:53

$color(brown)(bar(A'B') = sqrt((-1-17)^2 + (0-15)^2) = 23.43$

$A (1,4), B (7,9), C (2,6), " dilation factor " 3$

$A'C = 3 (a - c)$ , $A' - c = 3a - 2c$

$A'((x),(y)) = 3((1),(4)) - 2((2),(6)) = ((-1),(0))$

$B'C = 3 (b - c)$ , $B' - c = 3b - 2c$

$B'((x),(y)) = 3((7),(9)) - 2((2),(6)) = ((17),(15))$

Length of the line segment

$color(brown)(bar(A'B') = sqrt((-1-17)^2 + (0-15)^2) = 23.43$

A line segment has endpoints at (1 ,4 )(1,4)(1 ,4 ) and (7 ,9 )(7,9)(7 ,9 ). The line segment is dilated by a factor of 3 33 around (2 ,6 )(2,6)(2 ,6 ). What are the new endpoints and length of the line segment?