Question

1. the graph shows the relationship between the diameter and the circumference of a circle with the point $(1,\pi)$ shown. find 3 more points that are on the line.

Explanation:

Step1: Find the equation of the line

The relationship between the circumference \(C\) and diameter \(d\) of a circle is \(C=\pi d\) (since the formula for the circumference of a circle is \(C = \pi d\), and when \(d = 1\), \(C=\pi\times1=\pi\)).

Step2: Substitute \(d = 2\)

When \(d = 2\), \(C=\pi\times2 = 2\pi\). So the point is \((2,2\pi)\).

Step3: Substitute \(d=3\)

When \(d = 3\), \(C=\pi\times3=3\pi\). So the point is \((3,3\pi)\).

Step4: Substitute \(d = 4\)

When \(d = 4\), \(C=\pi\times4 = 4\pi\). So the point is \((4,4\pi)\).

Answer:

\((2,2\pi)\), \((3,3\pi)\), \((4,4\pi)\)