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

1 Answer
Nov 2, 2016

"the new end points of line segment are:(-8,27),(12,19)"
"the length of line segment is :"sqrt 464

Explanation:

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"the point of D(4,3) is dilatation point"

"the point F is image of B"

"distance between BC is :"7-3=4

"distance between FG is :"4*"factor"=4*4=16

"y coordinate of F is :" 3+16=19

"distance between DC is :"6-4=2

"distance between DG is :"2*"factor"=2*4=8

"x coordinate of F is :"4+8=12

"coordinates of F are :"F(12,19)

"The point of E is image of A"

"distance between AH is:"9-3=6

"distance between EI is:"6*"factor"=6*4=24

"y coordinate of E is :"3+24=27

"distance between HD is :"4-1=3

"distance between ID is :"3*"factor"=3*4=12

"the x coordinate of E is :"4-12=-8

"coordinates of E are :"E(-8,27)

"length of line segment AB :"

bar (AB)=sqrt((6-1)^2+(7-9)^2)

bar (AB)=sqrt(25+4)=sqrt(29)

"length of line segment EF:"

bar (EF)=sqrt((12+8)^2)+(19-27)^2

bar (EF)=sqrt(400+64)=sqrt(464)