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In (triangle ) ABC, AB = x, BC = y, and CA = 2x. A similarity transformation with a scale factor of 0.5 maps (triangle) ABC to (triangle) MNO, such that vertices M, N, and O correspond to A, B, and C, respectively. If OM = 5, what is AB?

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If a similarity transformation with a scale factor of 0.5 maps ΔABC to ΔMNO, such that vertices M, N, and O correspond to A, B, and C, respectively, then

[tex]MN=0.5\cdot AB,\\NO=0.5\cdot BC,\\OM=0.5\cdot CA.[/tex]

Given AB = x, BC = y, and CA = 2x, you can write

[tex]MN=0.5\cdot AB=0.5x,\\NO=0.5\cdot BC=0.5y,\\OM=0.5\cdot CA=0.5\cdot 2x=x.[/tex]

Since OM = 5, you can find x: OM=x=5. Then AB=x=5.

Answer: AB=5.

The value of the length AB when OM = 5 is calculated as; AB = 5

How to find lengths in Transformations?

We are given;

AB = x; This has a scale factor of 0.5.

BC = y;  This has a scale factor of 0.5.

CA = 2x; This has a scale factor of 0.5.

Thus, after transformation, we now have;

MN = x*0.5 = 0.5x

NO = y*0.5 = 0.5y

OM = 2x*0.5 = x

Now, if AM = 5, It means that;

AB = x =5

Read more about Transformations at; https://brainly.com/question/8474805

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