What is a Dilation in Geometry?
A dilation is a stretch or a shrink of a figure, so you’re making a shape bigger or smaller, but it’ll still be similar to the original shape. Therefore, it will be proportional to the original shape. Let’s look at an example. With the center of dilation at the origin, graph the dilation of triangle DEF with a scale factor of 2, so that means we’re going to be making our image larger because we’re going to be multiplying all of our coordinates by 2.
First, let’s find our coordinates of triangle DEF. Let’s start with point D. D is at (1, 2), E is at (negative 2, negative 2), and F is at (2, negative 1). Now we’re going to dilate our image by multiplying each one of these coordinates by our scale factor, which is 2.
Our new point D will be 1 times 2, which is 2, and 2 times 2, which is 4. Our new point E, negative 2 times 2, negative 4, and again negative 2 times 2, negative 4. Our new point F, 2 times 2 is 4, and negative 1 times 2 is negative 2. Now we can graph our dilation. Our new point D is at (2,4) (over 2, up 4). Our new point E is at (negative 4, negative 4), (negative 4, negative 4) and our new point F Is at (4, negative 2) (4, negative 2).
Now all we have to do is connect the dots for our new triangle, so there’s our dilation of triangle DEF about the origin.