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These two figures are the image and pre-image of a dilation. Find the length of the missing sides.

These two figures are the image and pre-image of a dilation. Find the length of the-example-1

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The missing side length in the second triangle is x = 2 + 1/2 = 5/2 inches.

In a dilation, the ratio of corresponding side lengths is always equal to the scale factor.

Therefore, we can set up the following proportion:

4/2 = (y+1)/x

Solving for x, we get:

x = (2 * (y+1)) / 4

x = y + 1/2

Now we can substitute the value of x back into the second triangle to find the missing side length:

y + 1 = 3

y = 2

Therefore, the missing side length in the second triangle is x = 2 + 1/2 = 5/2 inches.

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