[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.