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.
Enlargement
k>1
Reduction
0
Same
k=1
When the center of dilation in the coordinate plane is the origin, each coordinate of the preimage is multiplied by the scale factor k to find the coordinates of the image.
ccc
Preimage & & Image [0.5em]
(x,y)& ⇒ & ( kx, ky)
Now, let's find the coordinates of the vertices of BCDE after a dilation with a scale factor k= 13. Since our scale factor is less than 1, the dilation is a reduction.
Dilation With Scale Factor k= 13
Preimage
Multiply by k
Image
B(3,3)
( 1/3(3), 1/3(3))
B'(3/3,3/3)=(1,1)
C(3,6)
( 1/3(3), 1/3(6))
C'(3/3,6/3)=(1,2)
D(6,6)
( 1/3(6), 1/3(6))
D'(6/3,6/3)=(2,2)
E(6,3)
( 1/3(6), 1/3(3))
E'(6/3,3/3)=(2,1)
We can now plot the obtained points and connect them with segments to draw the image.
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.
