anonymous
  • anonymous
Find the circumcenter of triangle ABC with A(1,6), B(1,4), and C(5,4).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
|dw:1434588974015:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1434588988805:dw|

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More answers

jim_thompson5910
  • jim_thompson5910
Draw a segment from A to B |dw:1434589038187:dw|
jim_thompson5910
  • jim_thompson5910
what is the midpoint of this segment?
jim_thompson5910
  • jim_thompson5910
do you know the midpoint formula @iSpiffy2wice ?
anonymous
  • anonymous
no I dont :/
jim_thompson5910
  • jim_thompson5910
you add up the corresponding coordinates and then divide by 2
jim_thompson5910
  • 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
  • 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
  • jim_thompson5910
midpoint of AB is (1,5) |dw:1434589451464:dw|
jim_thompson5910
  • jim_thompson5910
making sense?
anonymous
  • anonymous
yes it is
jim_thompson5910
  • jim_thompson5910
so what is the midpoint of segment BC ?
anonymous
  • anonymous
3,5/?
jim_thompson5910
  • 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
  • jim_thompson5910
|dw:1434589662988:dw|
jim_thompson5910
  • 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
  • jim_thompson5910
the perpendicular bisectors cross at (3,5) so that is the circumcenter |dw:1434589790411:dw|
jim_thompson5910
  • 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
  • anonymous
thank you :O
anonymous
  • anonymous
can you help me w/ another?
jim_thompson5910
  • jim_thompson5910
sure, one more
jim_thompson5910
  • jim_thompson5910
oh wait, the radius isn't 2, so ignore that portion
anonymous
  • anonymous
is the attached file correct or no? D:
1 Attachment
jim_thompson5910
  • jim_thompson5910
were you able to find the value of x? if so, what is x equal to?
anonymous
  • anonymous
if were being honest no, I just guessed :/
jim_thompson5910
  • 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
  • anonymous
i have literally no idea what you just typed DD:
jim_thompson5910
  • jim_thompson5910
the three sides are AB, BC, and AC |dw:1434590337740:dw|
jim_thompson5910
  • jim_thompson5910
example: here is segment AB |dw:1434590361550:dw|
jim_thompson5910
  • jim_thompson5910
I added up AB, BC, and AC then I set all that equal to 30 since that is the perimeter
jim_thompson5910
  • jim_thompson5910
|dw:1434590403402:dw|
jim_thompson5910
  • jim_thompson5910
are you able to solve 5x-7+3x+1+4x = 30 for x ?
anonymous
  • anonymous
im trying but i dont really get it :/
anonymous
  • anonymous
12x-6? :-/
jim_thompson5910
  • jim_thompson5910
do you see how I did AB + BC + AC = perimeter ?
jim_thompson5910
  • jim_thompson5910
yeah 12x - 6 = 30
jim_thompson5910
  • jim_thompson5910
add 6 to both sides 12x - 6 = 30 12x - 6+6 = 30+6 12x+0 = 36 12x = 36
jim_thompson5910
  • jim_thompson5910
what's next?
anonymous
  • anonymous
BC??
anonymous
  • anonymous
snt that what we do next :L
jim_thompson5910
  • jim_thompson5910
well if 12 times ______ = 36, then what goes in the blank?
anonymous
  • anonymous
3
jim_thompson5910
  • jim_thompson5910
yep x = 3
jim_thompson5910
  • jim_thompson5910
we then use this x value to find AB, BC, & AC
jim_thompson5910
  • 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
  • jim_thompson5910
what is the length of BC?
anonymous
  • anonymous
it looks like an equilateral so 8 aswell? :L
jim_thompson5910
  • jim_thompson5910
don't base things off the picture alone my picture isn't to scale
jim_thompson5910
  • jim_thompson5910
use BC = 3x+1 and plug in x = 3
anonymous
  • anonymous
34? ://
jim_thompson5910
  • jim_thompson5910
BC = 3x+1 BC = 3*3+1 ... replace x with 3 BC = ???
anonymous
  • anonymous
OH 10
jim_thompson5910
  • jim_thompson5910
yep AB = 8 BC = 10 |dw:1434590954554:dw|
jim_thompson5910
  • jim_thompson5910
and finally, how long is AC ?
jim_thompson5910
  • jim_thompson5910
use the algebraic expression they give you
anonymous
  • anonymous
12?
jim_thompson5910
  • jim_thompson5910
good |dw:1434591008920:dw|
jim_thompson5910
  • jim_thompson5910
Rule: with any triangle... the largest angle is opposite the largest side the smallest angle is opposite the smallest side
anonymous
  • anonymous
so itd be |dw:1434590964987:dw| right?
jim_thompson5910
  • jim_thompson5910
no
jim_thompson5910
  • jim_thompson5910
|dw:1434591107541:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1434591138247:dw|
anonymous
  • anonymous
C A B?
jim_thompson5910
  • jim_thompson5910
correct
jim_thompson5910
  • 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
  • jim_thompson5910
if anything, the triangle probably looks like this |dw:1434591253370:dw|
anonymous
  • anonymous
thanks for bearing with me and helping me!!
jim_thompson5910
  • jim_thompson5910
you're welcome

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