Dilation with respect to the origin by a scale factor of 14
Practice makes perfect
We want to describe the relationship between the given points in terms of dilations.
A( 8, 12) → C(2,3)A dilation is a transformation in which a figure is made larger or smaller with respect to a point called the center of dilation. To find the image of a point after a dilation we need to multiply its coordinates by a scale factor k.
ccc
Preimage & & Image [0.5em]
(x,y)& ⇒ & ( kx, ky)
Notice that the coordinates of C are one-fourth of the coordinates of A.
A( 8, 12) → C(1/4* 8,1/4 * 12)
This means that the point C is a dilation with respect to the origin by a scale factor of 14.
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.
For those interested in learning more about other transformations, you can read more about them on the following pages.
