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

1 Answer
Jim G.
Jun 23, 2017

(10,6),(6,30),~~24.33

Explanation:

"let " A(4,3),B(3,9),D(2,2)" and " A',B'
"be the image of A and B under the dilatation"

vec(DA)=ula-uld=((4),(3))-((2),(2))=((2),(1))

rArrvec(DA')=color(red)(4)vec(DA)=color(red)(4)((2),(1))=((8),(4))

rArrA'=(2+8,2+4)=(10,6)

vec(DB)=ulb-uld=((3),(9))-((2),(2))=((1),(7))

rArrvec(DB')=color(red)(4)vec(DB)=color(red)(4)((1),(7))=((4),(28))

rArrB'=(2+4,2+28)=(6,30)

|A'B'|=sqrt((6-10)^2+(30-6)^2)=sqrt592

rArr|A'B'| ~~24.33" to 2 decimal places"

Related questions
See all questions in Dilations or Scaling around a Point
Impact of this question
1765 views around the world
You can reuse this answer
Creative Commons License