A dilation can be an enlargement, a reduction, or the same size as the preimage. Which type of dilation it is depends on the value of the scale factor k.
ccc
Preimage & & Image [0.5em]
(x,y)& ⇒ & ( kx, ky)
Now, let's find the coordinates of the vertices of QRTU after a dilation with a scale factor k= 13.
Dilation With Scale Factor k= 13
Preimage
Multiply by k
Image
Q(- 3,0)
( 1/3(- 3), 1/3(0))
Q'(- 3/3,0)=(- 1,0)
R(- 3,6)
( 1/3(- 3), 1/3(6))
R'(- 3/3,6/3)=(- 1,2 )
T(4,6)
( 1/3(4), 1/3(6))
T'(4/3,6/3)=(4/3,2 )
U(4,0)
( 1/3(4), 1/3(0))
U'(4/3,0)
We can now plot the obtained points and connect them with segments to draw the image.
Since the scale factor k is less than 1 and greater than 0, the dilation is a reduction.
Checking Our Answer
To check our answer, we can draw rays from the origin through the vertices of the original figure. The vertices of the dilation should lie on those rays.
