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Dilation

In this video, you will learn how to do a dilation and graph the new image.

Dilation: Transformation of an image that is different in size but proportionate to the original figure.

Dilation Notation:
Dk(x,y) \rightarrow (kx, ky) where k is the scale factor

Apply a dilation by a scale factor of 3 to triangle ABC with coordinate points of A(-2,1), B(2,2), and C(1,-2) with the center located at the origin.

Using the dilation notation and the scale factor of 3, we can easily determine the coordinate points of the image by multiplying the x-value by k and the y-value by k.

A(-2,1) \rightarrow A'(-6,3)
B(2,2) \rightarrow B'(6,6)
C(1,-2) \rightarrow C'(3,-6)

Dilation

Video-Lesson Transcript

Let’s go over dilations.

Dilations are denoted by capital letter D with some number k before whatever it is we’re dilating.

D_{k} (x, y)

This k is our factor of dilation or also known as scaled factor.

When we do the scale factor, we just have to multiply all the coordinates by that scale factor.

D_{k} (x, y) \rightarrow (kx, ky)

For example,

D_{4} (2, 5) \rightarrow (8, 20)

We can see that dilation resulted in a larger coordinate. A larger x value and a larger y value.

If the scale factor is less than one:

D_{\dfrac{1}{2}} (2, 8) \rightarrow (1, 4)

Here, the numbers went down.

When we dilate a shape, if k is bigger than 1 such as 4, the shape is going to be bigger.

But if the scale factor is less than 1 such as \dfrac{1}{2}, then the shape is going to be smaller.

Let’s take this triangle ABC and dialte it with a scale factor of 3.

D_3 \triangle {ABC}

Let’s first write down our coordinates.

A (-2, 1) \rightarrow A^\prime (-6, 3)
B (2, 2) \rightarrow B^\prime (6, 6)
C (1, -2) \rightarrow C^\prime (3, -6)

We just multiplied all coordinates by 3.

Now, let’s graph this.

This is what triangle ABC look like if we have a scale factor of 3.

We just simply multiplied the x and y coordinates by the scale factor of 3.

Also, 3 is bigger than 1 so we expect that the triangle will be bigger.

If the scale factor is less than 1 then the triangle will be smaller than the original, depending on what the scale factor is.