Question

how do i find the center of a circle on the coordinate plane?

Answer 1

Do you have an equation for the circle?

Answer 2

no

Answer 3

so you have the graph then?

Answer 4

yes

Answer 5

can you post it

Answer 6

yes it will take me a moment tho

Answer 7

alright

Answer 8

https://mail-attachment.googleusercontent.com/attachment/u/0/?ui=2&ik=096b789edb&view=att&th=13c54ebdbddada58&attid=0.0&disp=inline&safe=1&zw&saduie=AG9B_P8jfrhW98RmuQ_LbXp4lw6m&sadet=1358634443563&sads=ZnPHZpnpF7RBy_zUrjWevjO-7d4

Answer 9

do you know how to find the equation of perpendicular bisectors?

Answer 10

we have to write that using the midpoint and slope which we already found we just don't know how to write the equation

Answer 11

To find the equation, you use the general form

y = mx+b

Example:

Say you know that the slope is 2 and it goes through the point (5,7)

y = mx+b

y = 2x + b ... plug in the slope m = 2

7 = 2*5 + b ... plug in x = 5 and y = 7, this is from the point (5,7)

7 = 10 + b

7 - 10 = b

-3 = b

b = -3

Therefore, the equation that goes through (5,7) and it has a slope of 2 is y = 2x - 3

Answer 12

So if you have the perpendicular slopes and the midpoints, then you can find the equations of the perpendicular bisectors

You only need to do 2 equations for the 2 (out of 3) perpendicular bisectors because you only need 2 lines to have them intersect at the point...which is the center of the circle

Answer 13

we are working it out right now. thank you!

Answer 14

you're welcome

Answer 15

let me know what you get

Answer 16

for Line AB we got b = 2 so the equation would be y=1x-2

Answer 17

because the slop of AB = 1

Answer 18

it should be +2

y = mx + b

y = 1x + b

3 = 1*1 + b

3 = 1 + b

3 - 1 = b

2 = b

b = 2

Line through A and B: y = x + 2

Answer 19

yes

Answer 20

The midpoint of AB is (2,4)

The perpendicular slope of line AB is -1

y = mx + b

y = -1x + b

4 = -1*2 + b

4 = -2 + b

4 + 2 = b

6 = b

b = 6

So the equation of the perpendicular bisector of AB is y = -x + 6

Answer 21

Do the same to find the equation of the perpendicular bisector of AC or BC (you only need more more equation)

Answer 22

okay we'll work on that and get back to you thank you

Answer 23

np

Answer 24

equation for the perpendicular bisector of BC is Y=-2x+11

Answer 25

that's the equation of the line that goes through points B and C

Answer 26

it is NOT the equation of the perpendicular bisector of BC

Answer 27

you would need

a) the perpendicular slope

and

b) the midpoint of BC


to find the equation of the perpendicular bisector of BC

Answer 28

perpendicular slop is 1/2 and the midpoint of BC (4,3)

Answer 29

now use those two facts to find the perpendicular bisector of BC

Answer 30

y=1/2x+1

Answer 31

good

Answer 32

so you have these two perpendicular bisector equations:


y = -x + 6
y=1/2x+1

Answer 33

solve this system any way you can to find the point of intersection

this point of intersection is the center of the circle

Answer 34

how do we find the point of intersection?

Answer 35

well y is both -x+6 and it is 1/2x+1

so because of that you can say

-x + 6 = 1/2x + 1

Answer 36

solve for x

Answer 37

i don't think its right but i got x=3.3 repeating

Answer 38

that's correct, or 10/3

Answer 39

now that you know x, use it to find y

Answer 40

YES!!!!!!

Answer 41

how do we find Y?

Answer 42

I would stick with the fraction

Answer 43

y = -x + 6

y = -10/3 + 6 ... plug in x = 10/3

y = -10/3 + 6/1

y = -10/3 + (6/1)*(3/3)

y = -10/3 + 18/3

y = (-10 + 18)/3

y = 8/3

So the point of intersection is (10/3, 8/3)

This means that the center of the circle is the point (10/3, 8/3)

Answer 44

thank you so much that makes sense now

Answer 45

you're welcome

Answer 46

so each point is 1.4 away from the center which means the raduis is 1.4

Answer 47

no, the radius isn't 1.4

Answer 48

how? im confused!

Answer 49

find the distance from point A (1,3) to the center (10/3, 8/3) using the distance formula

Answer 50

i did and i got the sqaure root of 2 which is 1.4

Answer 51

d = sqrt( (x1-x2)^2 + (y1 - y2)^2 )

d = sqrt( (1-10/3)^2 + (3 - 8/3)^2 )

d = sqrt( (-7/3)^2 + (1/3)^2 )

d = sqrt( 49/9 + 1/9 )

d = sqrt( 50/9 )

d = 2.3570226

Answer 52

So the radius is roughly 2.3570226 units

it is exactly sqrt( 50/9 ) units

Answer 53

oh i see

Answer 54

not sure how you got sqrt(2)

Answer 55

i don't what im doing. our teacher hasn't taught us this

Answer 56

you haven't learned the distance formula yet?

Answer 57

we've learned that but she gave us a this project and never showed us how to find the center of a circle using points located on the circle

Answer 58

thank you for all your help

Answer 59

oh that's strange, but I'm glad to be of help

Answer 60

okay. last question. give possible coordinates of another point on the circle

Answer 61

we know the center and the radius

so we can use this general equation (x-h)^2 + (y-k)^2 = r^2

to find the equation of the circle

Answer 62

(h,k) is the center

r is the radius

Answer 63

so what is the equation of the circle?

Answer 64

what numbers do i put in for the x and y

Answer 65

pick any number for x that's in between x = 1 and x = 5

so you can pick x = 4 for instance.

plug whatever x value you pick in for x, then solve for y

Answer 66

(4-10/3)^2 + (y-8/3)^2 = 50/9^2
2/3^2 + (y-8/3)^2 = 50/9^2

Answer 67

im stuck

Answer 68

(x-h)^2 + (y-k)^2 = r^2

(x-10/3)^2 + (y-8/3)^2 = (sqrt(50/9))^2 ... plug in the values of h, k and r

(4 - 10/3)^2 + (y-8/3)^2 = (sqrt(50/9))^2 ... plug in x = 4

(4 - 10/3)^2 + (y-8/3)^2 = 50/9

(2/3)^2 + (y-8/3)^2 = 50/9

4/9 + (y-8/3)^2 = 50/9

(y-8/3)^2 = 50/9 - 4/9

(y-8/3)^2 = 46/9

I'll let you finish

Answer 69

i got y = 2.51

Answer 70

(y-8/3)^2 = 46/9

y-8/3 = sqrt(46/9) or y-8/3 = -sqrt(46/9)

y = 8/3 + sqrt(46/9) or y = 8/3 - sqrt(46/9)

y = 4.9274433277 or y = 0.4058900056

Answer 71

So we have two points where x = 4

(4, 4.9274433277)

and

(4, 0.4058900056)

Answer 72

ohhhhh okay thanks so much jim jim!!!:D

Answer 73

yw

Answer 74

lol echo echo...jk