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- ayyookyndall

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- MeowLover17

Think of the diameter as a line, solve for the midpoint of that line to find the center.

- MeowLover17

And the radius is basically the length from the midpoint to the end of the circle, in this case being one of the other coordinates.

- MeowLover17

The formula would be

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## More answers

- MeowLover17

http://www.purplemath.com/modules/midpoint.htm here

- MeowLover17

Good luck thats all the information i can give.

- jim_thompson5910

where are you stuck? are you stuck on the formula given on the page MeowLover17 gave you?

- ayyookyndall

Yes, putting it in.

- jim_thompson5910

P(-10,-2) and Q(4,6)
the x coordinates of each point are -10 and 4
add them up: -10+4 = -6
divide the result by 2: -6/2 = -3
so the x coordinate of the midpoint is x = -3
Do the same for the y coordinates to get the y coordinate of the midpoint

- jim_thompson5910

very good

- ayyookyndall

Thats it for Part A?

- jim_thompson5910

so that's effectively what this formula
\[\LARGE (x_m, y_m) = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)\]
is saying "add up the corresponding coordinates and divide by 2 to get the midpoint "

- ayyookyndall

Okay, got it. :-)

- jim_thompson5910

yes the midpoint of P and Q is the center because P and Q lie on the same diameter
|dw:1432945083421:dw|

- jim_thompson5910

The radius can be found in 2 ways
a) find the distance from the midpoint, ie center, to P or Q (pick one)
b) find the distance from P to Q, then divide by 2

- ayyookyndall

Which one will be easier?

- jim_thompson5910

they're about equal in difficulty since you need to use the distance formula either way

- ayyookyndall

I guess lets do A

- jim_thompson5910

alright, so you can find the distance from the midpoint to P
OR
find the distance from the midpoint to Q

- ayyookyndall

Find the distance from the midpoint to P

- jim_thompson5910

use the distance formula
\[\large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]
to find the distance from the midpoint (-3,2) to point P(-10,-2)

- jim_thompson5910

(x1,y1) = (-3,2)
(x2,y2) = (-10,-2)

- jim_thompson5910

good, now take the square root of that

- jim_thompson5910

so the exact distance is \[\Large \sqrt{65}\]
notice how it says "If your answer is not an integer, express it in radical form"

- jim_thompson5910

"radical" is math term for "square root, cube root, fourth root, etc"

- ayyookyndall

Did I get it right?

- ayyookyndall

Can't I say 8.06

- jim_thompson5910

8.06 is the approximate distance, but they want the exact form

- jim_thompson5910

yes that's the radius in exact radical form

- ayyookyndall

Are we done or is there more?

- ybarrap

|dw:1432944559846:dw|

- jim_thompson5910

they just want the radius, so we're done

- jim_thompson5910

|dw:1432945973861:dw|

- jim_thompson5910

an integer is a whole number (not just any number)

- jim_thompson5910

example of integers: -3, -22, 5, 8, 0, 157
example of nonintegers: 2.7, 8.5, \(\large \sqrt{15}\), \(\large \pi\)

- ayyookyndall

Oh, I understand. Thank you! ;-)

- jim_thompson5910

np

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