yo wazzup so can you guys help me with this one problem? Thanks a bunch!
Problem:
Draw a circle whose center is at (1,2) so that the point (1,5) is a point on the circle. What is the circumference of the circle.
I don't get those problems!
Note that both points are on the line x=1, and are 3 units apart. So, the radius of the circle is r=3.
Now, C = 2pi*r
Hey there! I'd be happy to help you with this problem.
To find the circumference of a circle, we need to know its radius or diameter. In this case, we are given the center of the circle and a point on the circle. We can use this information to find the radius of the circle.
The center of the circle is given as (1,2), and the point (1,5) lies on the circle. The distance between the center and any point on the circle is equal to the radius of the circle.
To find the distance between two points in the coordinate plane, we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Applying this formula here, we can find the radius of the circle:
distance = sqrt((1 - 1)^2 + (5 - 2)^2)
= sqrt(0 + 9)
= sqrt(9)
= 3
Therefore, the radius of the circle is 3 units.
Now that we have the radius, we can calculate the circumference of the circle using the formula:
circumference = 2 * pi * radius
Remember, pi is a mathematical constant that is approximately equal to 3.14.
circumference = 2 * 3.14 * 3
= 18.84 units
So, the circumference of the circle is approximately 18.84 units.
I hope that helps! Let me know if you have any further questions.