Find the circumcenter of triangle ABC with A(1,6), B(1,4), and C(5,4).

- anonymous

Find the circumcenter of triangle ABC with A(1,6), B(1,4), and C(5,4).

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- schrodinger

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- anonymous

@jim_thompson5910

- jim_thompson5910

|dw:1434588974015:dw|

- jim_thompson5910

|dw:1434588988805:dw|

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## More answers

- jim_thompson5910

Draw a segment from A to B
|dw:1434589038187:dw|

- jim_thompson5910

what is the midpoint of this segment?

- jim_thompson5910

do you know the midpoint formula @iSpiffy2wice ?

- anonymous

no I dont :/

- jim_thompson5910

you add up the corresponding coordinates and then divide by 2

- jim_thompson5910

midpoint of A and B
x coordinate of A is 1
x coordinate of B is 1
add and divide by 2
(1+1)/2 = 2/2 = 1
so the x coord of the midpoint of AB is x = 1

- jim_thompson5910

y coordinate of A is 6
y coordinate of B is 4
add and divide by 2
(6+4)/2 = 10/2 = 5
so the y coord of the midpoint of AB is y = 5

- jim_thompson5910

midpoint of AB is (1,5)
|dw:1434589451464:dw|

- jim_thompson5910

making sense?

- anonymous

yes it is

- jim_thompson5910

so what is the midpoint of segment BC ?

- anonymous

3,5/?

- jim_thompson5910

B is (1,4)
C is (5,4)
x coords
(x1+x2)/2 = (1+5)/2 = 6/2 = 3
y coords
(y1+y2)/2 = (4+4)/2 = 8/2 = 4
the midpoint of BC is (3,4)

- jim_thompson5910

|dw:1434589662988:dw|

- jim_thompson5910

now that we have the midpoints of AB and BC, we construct the perpendicular bisectors of AB and BC
|dw:1434589744838:dw|

- jim_thompson5910

the perpendicular bisectors cross at (3,5)
so that is the circumcenter
|dw:1434589790411:dw|

- jim_thompson5910

|dw:1434589818240:dw|
my circle is a bit off since things aren't to scale
but the circle is centered at (3,5), has a radius of 2
this circle goes through A,B and C

- anonymous

thank you :O

- anonymous

can you help me w/ another?

- jim_thompson5910

sure, one more

- jim_thompson5910

oh wait, the radius isn't 2, so ignore that portion

- anonymous

is the attached file correct or no? D:

##### 1 Attachment

- jim_thompson5910

were you able to find the value of x? if so, what is x equal to?

- anonymous

if were being honest no, I just guessed :/

- jim_thompson5910

add up the three sides, and set that equal to 30
5x-7+3x+1+4x = 30
solve for x to get x = ??

- anonymous

i have literally no idea what you just typed DD:

- jim_thompson5910

the three sides are AB, BC, and AC
|dw:1434590337740:dw|

- jim_thompson5910

example: here is segment AB
|dw:1434590361550:dw|

- jim_thompson5910

I added up AB, BC, and AC
then I set all that equal to 30 since that is the perimeter

- jim_thompson5910

|dw:1434590403402:dw|

- jim_thompson5910

are you able to solve 5x-7+3x+1+4x = 30 for x ?

- anonymous

im trying but i dont really get it :/

- anonymous

12x-6? :-/

- jim_thompson5910

do you see how I did AB + BC + AC = perimeter ?

- jim_thompson5910

yeah 12x - 6 = 30

- jim_thompson5910

add 6 to both sides
12x - 6 = 30
12x - 6+6 = 30+6
12x+0 = 36
12x = 36

- jim_thompson5910

what's next?

- anonymous

BC??

- anonymous

snt that what we do next :L

- jim_thompson5910

well if 12 times ______ = 36, then what goes in the blank?

- anonymous

3

- jim_thompson5910

yep x = 3

- jim_thompson5910

we then use this x value to find AB, BC, & AC

- jim_thompson5910

For instance
AB = 5x-7
AB = 5*3 - 7 ... replace x with 3
AB = 15 - 7
AB = 8
|dw:1434590785410:dw|

- jim_thompson5910

what is the length of BC?

- anonymous

it looks like an equilateral so 8 aswell? :L

- jim_thompson5910

don't base things off the picture alone
my picture isn't to scale

- jim_thompson5910

use BC = 3x+1
and plug in x = 3

- anonymous

34? ://

- jim_thompson5910

BC = 3x+1
BC = 3*3+1 ... replace x with 3
BC = ???

- anonymous

OH 10

- jim_thompson5910

yep
AB = 8
BC = 10
|dw:1434590954554:dw|

- jim_thompson5910

and finally, how long is AC ?

- jim_thompson5910

use the algebraic expression they give you

- anonymous

12?

- jim_thompson5910

good
|dw:1434591008920:dw|

- jim_thompson5910

Rule: with any triangle...
the largest angle is opposite the largest side
the smallest angle is opposite the smallest side

- anonymous

so itd be |dw:1434590964987:dw| right?

- jim_thompson5910

no

- jim_thompson5910

|dw:1434591107541:dw|

- jim_thompson5910

|dw:1434591138247:dw|

- anonymous

C A B?

- jim_thompson5910

correct

- jim_thompson5910

In my drawing, all of the angles look the same (maybe 60 degrees?)
but again, my drawing isn't to scale so it's not a good idea to base everything off the drawing alone

- jim_thompson5910

if anything, the triangle probably looks like this
|dw:1434591253370:dw|

- anonymous

thanks for bearing with me and helping me!!

- jim_thompson5910

you're welcome

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