Question

How can I find the coordinates of a point if I know the distance that point is to another point, and I know the coordinates of the second point mentioned?

Answer 1

can i see?

Answer 2

Sure. One coordinate is (5,-1), and the distance from that to the unknown coordinate is 10.

Answer 3

Also the equation of the line is y = (4/3)x-7.66 if that helps

Answer 4

the distance is sqrt( [( 5 - x)^2 + (-1-y)^2] where (x,y) is the unknown point AND THIS = 10

SO WE CAN WRITE (5 - X)^2 + (-1 - y)^2 = 100

Answer 5

yes it does help - we couldnt find the coordinates without that.

we need to solve the system of equations

Answer 6

Yeah, I tried setting the distance formula with those values equal to the distance (10) but didn't know where to go from there

Answer 7

y = (4/3) x - 7.66
(5 - x)^2 + (-1-y)^2 = 100

Answer 8

thats a bit messy
use substitution for y from first equation into the second.

Answer 9

I'd use wolframalpha to do it.

Answer 10

https://www.wolframalpha.com/input/?i=Solve+system+of+equations+y+%3D+(4%2F3)x+-+7.66+,++(5+-+x)%5E2+%2B+(-1-y)%5E2+%3D+100

Answer 11

I may be wrong but so far I got 0=x^2-11.33x+68.34
The roots would be the possible x values right?

Answer 12

there are 2 possible points

Answer 13

yes

Answer 14

No
there are no real roots for that one

Answer 15

Yeah. I did something wrong

Answer 16

Oh I just saw your wolframalpha link. Thanks

Answer 17

I see what I did wrong

Answer 18

substituting

( 5 - x)^2 + (-1 - (4/3 x - 7.66)^2 = 100
(5 - x)^2 + (-(4/3)x + 6.66)^2 = 100

25 - 10x + x^2 + (16/9)x^2 - 24.54x + 44.3556)

and so on..

Answer 19

Thanks for your time. I got it.

Answer 20

yw