Answer: The possible cordinates (X,Y) of B can be found with the formula Y = √(8^2 - (X- 5)^2) - 7 where -3 ≤ X ≤ 13
Explanation:
The point A is located at (5, -7)
And we know that we have 8 units of difference between A and B.
The equation of a circle centerd in the point (x0, y0) is:
(x - x0)^2 + (y - y0)^2 = r2
where r is the radius of the circle
So we can draw a circle of 8 units around A, and get:
(X - 5)^2 + (Y - (-7))^2 = 8^2
So from this equation we can find all the possible values of B, for this we can isolate one of the variables in one side and get a function.
Y = √(8^2 - (X- 5)^2) - 7
So for a given value of X, you can find the value of Y. where you need to remember that (8^2 - (X-5)^2) can not be a negative number, so we must have that:
8^2 ≥ (X - 5)^2
So X can go from -3 (because (-3 - 5)^2 = 8^2)
to X = 13 (because (13 - 5)^2 = 8^2)
So X is in the range {-3, 13}