Question

Help?
Emily and Jaiden were on opposite sides of town, but saw the same fireworks on July 4th. Emily was one mile north of Jaiden. They determined that Emily was 0.5 mile from where they were shot off and Jaiden was 0.7 mile from where they were shot off.

a. Write an equation representing all of the points that are 0.5 mile from Emily.

b. Write an equation representing all of the points that are 0.7 mile from Jaiden.

Answer 1

I would plot their positions on a graph. To keep things simple, put Emily at the center of the graph, at the point (0,0).

a. Write an equation representing all of the points that are 0.5 mile from Emily.
that sounds like a circle with a radius of 0.5
can you look up the equation of a circle (use google or your textbook) and write down the equation of a circle whose center is at (0,0) and whose radius is 0.5 ?

Answer 2

@phi... (x-0)^2 + (y-0)^2= 0.25

Answer 3

looks good. I would simplify to just
x^2 + y^2 = 0.25

now for b)

if we put emily at (0,0), at what point do we put Jaiden ?

Emily was one mile north of Jaiden. which means Jaiden is 1 mile south of emily
I would put Jaiden at (0,-1) (same x but down 1 mile from Emily)

b. Write an equation representing all of the points that are 0.7 mile from Jaiden.

that would be a circle with a center at (0,-1) and radius 0.7

Answer 4

(x-0)^2 + (y-(-1)^2 =0.49

Answer 5

yes, simplify to
x^2 + (y+1)^2 =0.49

(you do know that y - -1 is y+1 right ?

Answer 6

yes I do, thanks! :)

Answer 7

is there more to this question ?

Answer 8

yeah

Answer 9

The equations you wrote put emily at (0,0). I want to be sure they did not tell you to use some other spot for the origin.

Answer 10

there is a third part to the whole question - but not to that one specifically.

Answer 11

I am guessing the next thing to ask is where were the fireworks shot from ?

Answer 12

yes

Answer 13

Emily was looking southeast to see the fireworks and Jaiden was looking northeast. Based on the coordinates given for Emily, E, and Jaiden, J, find the coordinates of the place where the fireworks were shot off, to the nearest tenth.

Answer 14

@phi

Answer 15

gack! they put Jaiden at the origin. can you re-do your circle equations ?

Answer 16

sure, but isn't Jaiden at the origin for the last part of the question?

Answer 17

I would use Jaiden at the origin for the first part... just in case. Who wants to argue with the teacher ?

Answer 18

haha true :) so just switch and put Emily at (0,1) and Jaiden at at (0,0) for the first two?

Answer 19

yes, you get
Emily : x^2 + (y-1)^2 = 0.25
Jaiden : x^2 + y^2 = 0.49

to find the point(s) where these circles intersect
x^2 + y^2 = 0.49
-( x^2 + (y-1)^2 = 0.25) subtract these equations