We want to determine if our friend is correct. Recall that to find the image of a vertex after a dilation with scale factor k, we multiply its coordinates by k.
ccc
Preimage & & Image [0.5em]
(x,y)& ⇒ & ( kx, ky)
Since the scale factor is 2, we will multiply the coordinates of â–ł ABC by 2.
Dilation With Scale Factor k=2
Preimage
Multiply by k
Image
A(2,5)
( 2(2), 2(5))
A'(4,10)
B(2,0)
( 2(2), 2(0))
B'(4,0)
C(4,0)
( 2(4), 2(0))
C'(8,0)
Notice that we got the same coordinate as our friend. Therefore, our friend is correct!
Extra
Everyday Examples
Now that we know more about dilations, notice that there are a lot of situations in real life where this transformation is very important. Let's see some examples!
Zoom in on a picture to see more details.
The pupils in our eyes dilate in response to the amount of light intake.
Architects have to increase the measurements of prototypes to construct a real building.
Detectives use dilations to increase the size of collected fingerprints for investigation.
More information about transformations can be found on the following pages.
