To determine the scale factor of dilation of the unit circle that passes through the point [tex]\((4,0)\)[/tex], follow these steps:
1. Identify the Original Radius:
The unit circle has a radius of 1 unit.
2. Identify the New Radius:
After dilation, the circle passes through the point [tex]\((4,0)\)[/tex]. This point lies on the circumference of the dilated circle. Since the point [tex]\((4,0)\)[/tex] is 4 units away from the origin (the center of the circle), the new radius of the dilated circle is 4 units.
3. Calculate the Scale Factor:
The scale factor of dilation is the ratio of the new radius to the original radius.
[tex]\[
\text{Scale Factor} = \frac{\text{New Radius}}{\text{Original Radius}}
\][/tex]
4. Substitute the Values:
[tex]\[
\text{Scale Factor} = \frac{4 \text{ units}}{1 \text{ unit}} = 4
\][/tex]
So, the scale factor of dilation is [tex]\(4\)[/tex].
The correct answer is:
[tex]\[ 4 \][/tex]
