Question

The unit circle has a radius of 1 unit and is centered at the origin. It is dilated so that it passes through the point . What is the scale factor?

a) 1/4
b) 1/3
c) 3
d) 4

Answer 1

The scale factor when a unit circle is dilated to pass through a point 4 units from the origin is 4, meaning the dilation is 1:4.

Step-by-step explanation:

The question asks about finding the scale factor when a unit circle with a radius of 1 is dilated to pass through a certain point. To solve a similar problem, you would set up a proportion such as 1:2=4:x, where 1 is the original dimension, 2 is the scale factor, and 4 is the scale dimension. Let's assume the point the circle must pass through is at a distance of 4 units from the origin. Since the original radius is 1, the new radius must be 4 to reach the point, which means the circle's size has increased by a factor of 4. Therefore, the scale factor is 4, or the dilation is 1:4.