Question

Please help me with this problem!! Solve the following problem. Suppose lighthouse A is located at the origin and lighthouse B is located at coordinates (0,6). The captain of a ship has determined that the ship's distance from lighthouse A is 2 and its distance from lighthouse B is 5. What are the possible coordinates for the ship? Please show all your work and calculations.

Answer 1

As you can see there are two position of the ship that could satisfy those distances from A and B. Does the diagram help and give you an idea how to solve?

Answer 2

sort of, but I know i need to use the distance formula in some way, but I dont know how

Answer 3

Exactly, we know that 5^2 = (0-x)^2 + (6-y)^2 and further we know
2^2 = (0 -x)^2 + (()-y)^2 There you see, you are using the distance formulas, two equations, two unknowns (x and y).......solvable.

Answer 4

Doing the math 25 = x^2 +y^2 -12y + 36 and
4 = x^2 + y^2 Now subtract those equations getting
-------------------------------------
21 = -12y + 36 Sprinkle with a little algebra getting
12y = 36 - 21 = 15
y = 15/12 = 5/4 or 1 1/4 Now you can solve for x.

Answer 5

To solve for x substitute the value for y in one of the formula, I would choose the
4 = x^2 + y^2 when you substitute you would get:
4 = x^2 + 25/16 note 25/16 is y^2 (5/4)^2
x^2 = 4 - 25/16 Leaving the rest to you to solve for x don't forget you will get
both a positive and a negative value when you take the square rt.

Answer 6

Can you do that last step?

Answer 7

okay, so the coordinates are (sqrt39/4, 5/4)?

Answer 8

Yes, but you have to pair . (sqrt39/4, 5/4) and (-sqrt39/4, 5/4) do you see the ship could be at either set.......see diagram.

Answer 9

If you see that there is two possible locations for the ship, I will give you a medal.

Answer 10

i do see this, but forgot to type it thank u for ur help b

Answer 11

Good luck with your studies.

Answer 12

Thank u good sir