# Thread: Help working with two points of a circle

1. ## Help working with two points of a circle

Hi all,

I'm currently preparing to resit a Math exam from a few years back I failed at college in order to graduate. I am weak at Math and haven't done it in sometime. I am having difficulty with the below kind of questions:

The diameter of a circle starts at (-101, -159) and ends at (-158, 62). What is the circumference of that circle with your answer rounded up to a whole number.

The answer for the above is 717 ± 1%, according to my Virtual learning environment, but I have no idea why. I tried using the distance formula to get the diameter, then divided the answer by 2 to get the radius which I then put in to the formula for getting the circumference.

Another question:
The radius of a circle starts at (173, -102) and ends at (53, -4). What is the area of that circle with your answer rounded up to a whole number.

The answer for the above question is 75,411 ± 1%. Is this the same as above and then just use the area of a circle formula instead?

I'd greatly appreciate if someone could run through these questions and explain how to get a (correct) number to plug in to the formulas from the two points.

Cheers.

2. ## Re: Help working with two points of a circle

The distance from (-101, -159) to (-152, 62) is $\displaystyle \sqrt{(-101+ 152)^2+ (-159- 62)^2}= \sqrt{51^2+ (-221)^2}= \sqrt{51442}= 226.81$. That is the diameter of the circle and the circumference is $\displaystyle \pi$ times the diameter (there is no reason to divide by 2 to get the radius. Using "$\displaystyle c= 2\pi r$ you would just multiply by 2 again.) so is $\displaystyle 3.1416(225.81)= 712.59$ which, rounded up to a whole number is 713, not "717". I have no idea why they have the "$\displaystyle \pm 1$%". There is nothing said about an error in the measurement. "

Similarly, the distance from (173, -102) to (53, -4) is $\displaystyle \sqrt{(173- 53)^2+ (-102+ 4)^2}= \sqrt{24004}= 153.932$. The area is $\displaystyle \pi r^2= 3.1415(153.932)^2= 75411$ "rounded up to a whole number". Again, I see no reason for the "$\displaystyle \pm 1$%".

3. ## Re: Help working with two points of a circle

Originally Posted by frick
The distance from (-101, -159) to (-152, 62) is $\displaystyle \sqrt{(-101+ 152)^2+ (-159- 62)^2}= \sqrt{51^2+ (-221)^2}= \sqrt{51442}= 226.81$.
That is the diameter of the circle and the circumference is $\displaystyle \pi$ times the diameter (there is no reason to divide by 2 to get the radius.
Using "$\displaystyle c= 2\pi r$ you would just multiply by 2 again.) so is $\displaystyle 3.1416(225.81)= 712.59$ which, rounded up to a whole number
is 713, not "717". I have no idea why they have the "$\displaystyle \pm 1$%". There is nothing said about an error in the measurement. "