Question

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

Answer 1

Please note that the options for the graphs are missing in the question posted. However, I will try my best to answer the question as there is just one graph that is possible.

Please find the two attached diagrams to get a better understanding of the answer provided here.

Let us consider the first diagram. Here, we have a circle with center O. The radius of the circle is $r$. Let the length of the arc be $l$ and it subtends an angle $\theta$ at the centre.

Now, we know that the relationship between arc length, $l$, radius, $r$ and angle subtended $\theta$ is given as:

$l=r\times \theta=r \theta$

Thus, the relationship is linear and the graph between $l$ and $\theta$ for a given $r$ will be a straight line whose slope will be given by $r$.

Now, we also know that the maximum arc length that a circle can possibly have is the circumference of the circle which is given by $2\pi r$ and that happens when the angle $\theta$ subtended at the center is equal to $2\pi$.

Keeping the information of the above two paragraphs please have a look at the second diagram.

This second diagram is the required graph as asked in the question.

Answer 2

Answer:

Answer C for Plato

Step-by-step explanation:

Based on the explanation above