Home > Geometry > Dilations or Scaling around a Point

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

Answer 1

New endpoints: Dilation of #(2,1) rarr (-1,1)#
#color(white)("New endpoints:")#Dilation of #(4,2) rarr (7,5)#
New line segment length: #4sqrt(5)" units"#

If the center of dilation is #C=(3,1)#
and original endpoints are
#{: (P=(2,1),color(white)("xxxxx"),Q=(4,2)), (vec(CP)=(2-3,1-1),,vec(CQ)=(4-3,2-1)), (color(white)(vec(CP))=(-1,0),,color(white)(vec(CQ))=(1,1)), ("dilated vector:",,"dilated vector:"), (4vec(CP)=(-4,0),,4vec(CQ)=(4,4)), (hat(P)=C+4vec(CP),,hat(Q)=C+4vec(CQ)), (color(white)(hat(P))=(-1,1),,color(white)(hat(Q))=(7,5)) :}#

The length of the dilated line segment is
#abs(hatPhatQ)=sqrt((7-(-1))^2+(5-1)^2)=sqrt(80)=4sqrt(5)#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Sadie Adams

The new endpoints of the line segment after dilation are (6, 1) and (10, 2). The length of the line segment is 4 units.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.