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

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Answer 1 · 2016-11-16T13:30:38

$please have a look the animation below$ $"please have a look the animation below"$

$The new end points of line segment are : F (16, 15), I (24, - 1)$ $"The new end points of line segment are :"F(16,15),I(24,-1)$

$Length of the line segment is : 17.89$ $"Length of the line segment is :"17.89$

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$the coordinates of point F:$ $"the coordinates of point F:"$

$C J \cdot factor = 3 \cdot 4 = 12$ $CJ*"factor"=3*4=12$

$4 + 12 = 16 the x coordinate of F$ $4+12=16" the x coordinate of F"$

$A J \cdot factor = 3 \cdot 4 = 12$ $AJ*"factor"=3*4=12$

$3 + 12 = 15 the y coordinate of F$ $3+12=15"the y coordinate of F"$

$F (16, 15)$ $F(16,15)$

$the coordinates of I Point:$ $"the coordinates of I Point:"$

$Z B \cdot factor = 5 \cdot 4 = 20$ $ZB*"factor"=5*4=20$

$4 + 20 = 24 the x coordinate of I$ $4+20=24" the x coordinate of I"$

$C Z \cdot factor = 1 \cdot 4 = 4$ $CZ*"factor"=1*4=4$

$3 - 4 = - 1 the y coordinate of I)$ $3-4=-1" the y coordinate of I")$

$I = (24, - 1)$ $I=(24,-1)$

$the length of line segment FI :$ $"the length of line segment FI :"$

FI=sqrt((16-24)^2+(15+1)^2)

$F I = \sqrt{64 + 256}$ $FI=sqrt(64+256)$

$F I = \sqrt{320}$ $FI=sqrt(320)$

$F I = 17.89$ $FI=17.89$

A line segment has endpoints at (7 ,6 )(7,6)(7 ,6 ) and (9 ,2 )(9,2)(9 ,2 ). The line segment is dilated by a factor of 4 44 around (4 ,3 )(4,3)(4 ,3 ). What are the new endpoints and length of the line segment?