Circle P is dilated by a scale

Answered question

2022-05-05

 Circle P is dilated by a scale factor of 1.5 to create circle P'. The circumference of circle P is x units.

Problem

What is the circumference in units of circle P'?

Answer & Explanation

xleb123

xleb123

Skilled2023-05-04Added 181 answers

Given that circle P is dilated by a scale factor of 1.5 to create circle P'. We need to find the circumference of circle P' in terms of the circumference of circle P.
Let the radius of circle P be r, then the circumference of circle P is given by:
CP=2πr
After dilation with a scale factor of 1.5, the radius of circle P' becomes 1.5r. Therefore, the circumference of circle P' is given by:
CP=2π(1.5r)=3πr
Thus, we see that the circumference of circle P' is 3 times the circumference of circle P. Therefore, if the circumference of circle P is x units, then the circumference of circle P' is 3x units.
In summary, the circumference of circle P' is 3x units.

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