A line segment has endpoints at (1 ,4 )(1,4) and (4 , 9)(4,9). The line segment is dilated by a factor of 1/3 13 around (4 , 2)(4,2). What are the new endpoints and length of the line segment?

1 Answer
sankarankalyanam
Jun 7, 2018

color(brown)("Length of the line segment " color(blue)(bar(AB) " after dilation is " color(green)(1.94 " units"Length of the line segment ¯¯¯¯¯¯AB after dilation is 1.94 units

Explanation:

A (1,4), B(4,9). " Dilated by a factor of 1/3 around " C (4,2)A(1,4),B(4,9). Dilated by a factor of 1/3 around C(4,2)

bar(A'C) = (1/3) bar(AC)

A'C - c = (1/3)(a - c)

A' = a / 3 + (2/3)c

A'((x),(y)) = (1/3)((1),(4)) + (2/3)((4),(2)) = ((3),(8/3))

Similarly, B' = b / 3 + (2/3)c

B'((x),(y)) = (1/3)((4),(9)) + (2/3)((4),(2)) = ((4),(13/3))

Length of the line segment A'B' = sqrt((3-4)^2 + (8/3-13/3)^2)

vec(A'B') = 1.94 ' units"

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