A line segment has endpoints at $(7 ,2 )$ and $(3 ,4 )$ . The line segment is dilated by a factor of $6$ around $(4 ,5 )$ . What are the new endpoints and length of the line segment?

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Answer 1 · 2018-06-19T04:45:05

$color(maroon)(bar(A'B') = sqrt((22+2)^2 + (-13+1)^2) = 26.83$

$A (7,2), B (3,4), C (4,5), " dilation factor " 6$

$A'C = 6 (a - c)$ , $A' - c = 6a - 5c$

$A'((x),(y)) = 6((7),(2)) - 5((4),(5)) = ((22),(-13))$

$B'C = 6 (b - c)$ , $B' - c = 6b - 5c$

$B'((x),(y)) = 6((3),(4)) - 5((4),(5)) = ((-2),(-1))$

Length of the line segment

$color(maroon)(bar(A'B') = sqrt((22+2)^2 + (-13+1)^2) = 26.83$

A line segment has endpoints at (7 ,2 )(7 ,2 ) and (3 ,4 )(3 ,4 ). The line segment is dilated by a factor of 6 6 around (4 ,5 )(4 ,5 ). What are the new endpoints and length of the line segment?