Mathematics: Given two concentric circles (circles that have the same center point), with the inner circle having a radius of r1 and the outer one having a radius of r2 as shown, give a dilation that would map the inner circle onto the outer circle. Specify both the center of dilation and the scale factor.

Given two concentric circles (circles that have the

Ответ:

iyeshaik

04.03.2022

The center of dilation has a coordinate of (x,y) = (h,k) and the scale factor is . The transformation formula is $r^{2} = \frac{(x_{2}-h)^{2}+(y_{2}-k)^{2}}{(x_{1}-h)^{2}+(y_{1}-k)^{2}}$ .

How to define a dilation between two concentric circles

Two circles are concentric when they share the same center ( h, k ) but they have different radii ( $r_{1}, r_{2}$ ), where $r_{1}$ corresponds to the radius of the smaller circle. By analytic geometry we know that circles are modeled after this formula:

$(x-h)^{2}+(y-k)^{2} = r^{2}$ (1)

If we assume that the center of dilation is the center of both circles and the dilation use a scale factor of . Then, we have the following expression:

$r= \frac{r_{2}}{r_{1}}$

$r^{2} = \frac{(x_{2}-h)^{2}+(y_{2}-k)^{2}}{(x_{1}-h)^{2}+(y_{1}-k)^{2}}$ (2)

The center of dilation has a coordinate of (x,y) = (h,k) and the scale factor is . The transformation formula is $r^{2} = \frac{(x_{2}-h)^{2}+(y_{2}-k)^{2}}{(x_{1}-h)^{2}+(y_{1}-k)^{2}}$ . $\blacksquare$

To learn more on dilations, we kindly invite to check this verified question:

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Ответ:

taylorpayne525p8qxky

02.01.2020

Mathematics

3/15

Step-by-step explanation:

first you simply square root both parts of the fraction. You can start off by square rooting 9 which would be 3, and for 225, it would be 15. As a result, your simplified answer would be 3/15

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Given two concentric circles (circles that have the same center point), with the inner circle having a radius of r1 and the outer one having a radius of

r2 as shown, give a dilation that would map the inner circle onto the outer

circle. Specify both the center of dilation and the scale factor.

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