Question

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1

Answer 1

12 inches

Explanation:

Let us take the original radius of the circle be " x " .

Now here we are given that a scale factor of 3/4 is used to dilate the circle . This means the new radius will be 3/4 times of the original radius, that is 3/4x .

But according to question it is given to be 9 inches .

Therefore;

==> 3/4x = 9 inches

==> x = 9*4/3 inches

==> x = 12 inches

Hence the original radius of the circle was 12inches .

Answer 2

The radius of original circle is 12 inches.

Explanation:

In geometry, a scale factor refers to the proportional factor by which all the dimensions of an object are multiplied to create a similar but differently sized object.

In particular, in the context of a dilation, which is a type of transformation that changes the size of an object but not its shape, the scale factor determines how much larger or smaller the resulting image is compared to the original object.

If the scale factor used to create a dilated circle is 3/4, it means that the radius of the dilated circle is 3/4 times the radius of the original circle.

Let "x" be the radius of the original circle.

As the dilated circle has a radius of 9 inches, and the scale factor was 3/4, we can set up the following equation:

`\implies (3)/(4) x = 9`

To find the radius of the original circle, solve the equation for x:

`\implies 4\cdot (3)/(4) x = 4\cdot 9`

`\implies 3x=36`

`\implies (3x)/(3)=(36)/(3)`

`\implies x=12`

Therefore, the radius of original circle is 12 inches.