[G.SRT.1.b]

First, lets calculate the lengths of our line segments in this preimage. We can already see that

AB = 5 - 2 = 3
AC = 6 - 2 = 4

We can use the Pythagorean Theorem to find BC

AB² + AC² = BC²

3² + 4² = BC²

9 + 16 = BC²

25 = BC²

BC = 5

Objective

Common Core Text:

- [G.SRT.1.b] The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

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Explanation

Let's look at what happens to line segments

Example

In the following picture, the center of dilation is the origin. Perform a dilation on triangle ABC with a scale factor of 2, and explain the relationship between the lengths of the line segments in the preimage and image.

Now, lets calculate the lengths of our line segments in the image. We can already see that

A'B' = 10 - 4 = 6
A'C' = 12 - 4 = 8

We can use the Pythagorean Theorem to find BC

A'B'² + A'C'² = B'C'²

6² + 8² = B'C'²

36 + 64 = B'C'²

100 = B'C'²

B'C' = 10

Now let's perform the dilation

What's the ratio of image to preimage?

Looks like every ratio is 2. And wha-da-ya-know, that's our scale factor.

In conclusion

- The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

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