Question

A circle is drawn on the coordinate plane. It has a center at (2, 1) and passes through the point (2, 5). What is the approximate circumference of the circle?

Answer 1

First we need to find the radius. Using Pythagorean theorem we can find the radius which is the distance between the center and any point along the circle:

r=((5-1)^2+(2-2)^2)^(1/2)

r=(4^2-0^2)^(1/2)

r=4 units.

Circumference=2pr so our circumference is 8p units^2

Approximately 25.13 u^2

Answer 2

To find the circumference of a circle with a center at (2, 1) and passing through (2, 5), calculate the radius (4 units) and use the formula C = 2πr to get an approximate circumference of 25.13 units.

The student's question is about finding the approximate circumference of a circle on the coordinate plane with a given center and a point through which it passes. Knowing the center at (2, 1) and a point on the circumference at (2, 5), we can deduce that the radius of the circle is the distance in the y-coordinate, which is 4 units. To find the circumference, we use the formula C = 2πr, where r is the radius of the circle.

Substituting the given radius into the formula, we get:

C = 2π(4)

C = 8π

Approximating π as 3.14159, we can estimate the circumference:

C ≈ 8(3.14159)

C ≈ 25.13272

So the approximate circumference of the circle is 25.13 units.