Question

A circle with center L contains points J and K. Circle L is dilated by a factor of 2, resulting in a new circle with center P. Points M and N are on circle P such that central angle MPN has the same measure as central angle JLK. Which statement correctly identifies the relationship between the arc length of JK and the arc length of MN?

Answer 1

When a circle is dilated with a factor of 2, the arc length of MN will be twice as long as the arc length of JK.

Step-by-step explanation:

The relationship between the arc lengths of JK and MN depends on the dilation factor of circle L. When a circle is dilated, the radius is multiplied by the dilation factor. Since both JK and MN are radii of circle L, their lengths will also be multiplied by the dilation factor.

Therefore, if the dilation factor is 2, the arc length of MN will be twice as long as the arc length of JK.

Thus, the correct statement is that the arc length of MN is twice as long as the arc length of JK.