Question

HELP ME WITH THIS PROBLEM PLZ

Answer 1

helpp

Answer 2

we can do this

Answer 3

it is kind of a pain, but totally doable
first we need the point \((x,y)\) equidistant from the three points
if it is equidistant from \((1,3)\) and \((5,11)\) then we know by the distance formula that
\[(x-1)^2+(y-3)^2=(x-5)^2+(y-11)^2\]

Answer 4

okay

Answer 5

soo do i just plug in the points?

Answer 6

oh no!! we have a few more steps

Answer 7

multiply all that mess out and you get
\[8 x+16 y-136 = 0\]

Answer 8

divide by 4 and get
\[2x+4y=34\] now hold on to that, we have to do it again

Answer 9

ok

Answer 10

this time we use the third point \((11,4)\) and the distance formula gives
\[(x-11)^2+(y-4)^2=(x-5)^2+(y-11)^2\]

Answer 11

multiply all that mess out, and you get
\[-12 x+14 y = 9\]

Answer 12

Multiplying what exactly can you be more specific plz? sorry

Answer 13

that means we have to solve two equations
\[x+2y=17\] and \[-12x+14y=9\]

Answer 14

oh i mean expand, and combine like terms

Answer 15

ooh ok

Answer 16

here it is for the second one
\[(x-11)^2+(y-4)^2=(x-5)^2+(y-11)^2\] expanding gives
\[x^2-22x+121+y^2-8yt+16=x^2-10x+25+y^2-22y+121\]

Answer 17

i got a typo there, but you get the idea
get rid of the \(x^2\) and \(y^2\) from both sides
add up
etc

Answer 18

ok

Answer 19

hmm i wonder if i made a mistake, because my answer is very ugly
hold on a sec

Answer 20

alright

Answer 21

no i got the same ugly answer twice, once using wolfram

Answer 22

http://www.wolframalpha.com/input/?i=%28x-1%29^2%2B%28y-3%29^2%3D%28x-5%29^2%2B%28y-11%29^2%2C%28x-5%29^2%2B%28y-11%29^2%3D%28x-11%29^2%2B%28y-4%29^2
\[x=\frac{110}{19},y=\frac{213}{38}\]

Answer 23

so this is the answer?

Answer 24

What other steps do i need to do?

Answer 25

now that we have the center of the circle (presumably the shape is a circle) then you have to find the equation for the circle

so you need the distance from the center to any of the three other points
they should all be the same

Answer 26

How do i find the equation??

Answer 27

\[(x-\frac{110}{19})^2+(y-\frac{213}{38})^2=r^2\] we need \(r^2\)

Answer 28

i can't believe they gave a problem with such an ugly answer

Answer 29

lol.. but how do find the radius? can set it up so i can figure it out

Answer 30

typo!!
\[r^2=(\frac{110}{19}-1)^2+(3-\frac{213}{38})^2\]

Answer 31

Okay is there any other steps after this???

Answer 32

use a calculator
if it was me, i would cheat

Answer 33

i mean cheat for the whole problem
hold on

Answer 34

http://www.wolframalpha.com/input/?i=circle+through+%281%2C3%29%2C+%285%2C11%29%2C%2811%2C4%29

Answer 35

ok

Answer 36

Oh thank you :)

Answer 37

there we have it
btw you are the second person lately to use myers briggs
whats up with that??

Answer 38

I am? lol I didnt notice anyone else using it.

Answer 39

not yours, but some other one

Answer 40

infj

Answer 41

oh ok lol