Dilation with respect to the origin by a scale factor of 34
Practice makes perfect
We want to describe the relationship between D(6,9) and A( 8, 12) in terms of dilations. When the center of dilation is the origin, each coordinate of the preimage is multiplied by the scale factor k to find the coordinates of the image. To find D, we need to multiply the coordinates of A by a k.
D( k* 8, k* 12) = D (6,9)We can find k by writing the x-coordinate of the image D as the product of 8 multiplied by k.
k* 8=6
Now, let's use inverse operations to isolate k on one side of the equation.
This means that the point D is a dilation with respect to the origin by a scale factor of 34.
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.
