Question

Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle withradius r?

Answer 1

Step-by-step explanation

The length of an arc is given by the formula

`l=(\theta)/(360)*2\pi r`

where θ is the angle at the center of the circle that subtends the arc.

If the central angle has a measure of π/2(90°), then the length of the arc will be one-fourth of the total, while if the measure of the angle is π(180°), then the length of the arc will be half of the total.

Similarly, if the measure of the angle is 3π/4, then the length of the arc will be three-fourth of the total, while if the measure of the angle is 2π(360°), then the length of the arc will be 2πr.

Answer: Option C