Let's call the coordinates of the treasure (x, y) .
The treasure is 10 yards away from (0, 0) ,
and we know that the distance between any two points = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
Using the points (x, y) and (0, 0) and a distance of 10 , we have...
10 = \(\sqrt{(x-0)^2+(y-0)^2}\,=\,\sqrt{x^2+y^2}\) → 100 = x2 + y2
The treasure is 10 yards from (15, 0) . So we know that
10 = \(\sqrt{(x-15)^2+(y-0)^2}\,=\,\sqrt{(x-15)^2+y^2}\) → 100 = (x - 15)2 + y2
Now we have two equations and two variables.
They both equal 100, so we can set these equal.
x2 + y2 = (x - 15)2 + y2
x2 = (x - 15)2
x = ±(x - 15)
x = x - 15 or x = -(x - 15)
0 = -15 x = -x + 15
false 2x = 15
x = 15 / 2
Plug this value for x into x2 + y2 = 100 to find the value of y .
(15 / 2)2 + y2 = 100
y2 = 100 - (15 / 2)2
y = ±√[ 100 - (15 / 2)2 ]
y ≈ 6.6
Since there are only positive values of y on the map, the coordinates are ≈ (7.5, 6.6)
