Final answer:
The coordinates of the oak tree, which is equidistant from point A(-35, -32) as point B(29, -16), are found using the midpoint formula. Solving the system of equations, the coordinates are C(-99, -64).
Step-by-step explanation:
The question asks to find the coordinates of a point (the oak tree) that is at the same distance from point A(-35,-32) as point B(29,-16) but in the opposite direction.
To find the coordinates of the oak tree, we can use the midpoint formula which states that the midpoint, M, between two points X(x1, y1) and Y(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2).
Since point A is the midpoint between point B and the oak tree, we can set up a system of equations to find the coordinates of the oak tree (let's call it point C(x, y)):
- (x + 29)/2 = -35
- (y - 16)/2 = -32
By solving these equations, we can find the coordinates of point C:
- x = -35 * 2 - 29 = -99
- y = -32 * 2 + 16 = -64
Therefore, the coordinates of the oak tree are C(-99, -64).