Answer:
(2, 1)
Explanation:
If the line segment AB is partitioned so that the ratio of AP to PB is 2 : 1, then point P is two-thirds of the way along AB.
Point A is located at (-2, 3) and point B is located at point (4, 0).
Since the difference between the x and y values of points A and B are multiples of 3, we can visually partition AB into 3 sections of equal length by placing points at (0, 2) and (2, 1).
Therefore, as point P is two-thirds of the way along AB, point P is located at (2, 1).
To prove this mathematically, we can use the Section Formula for Internal Division:

Given values:
- (x₁, y₁) = A = (-2, 3)
- (x₂, y₂) = B = (4, 0)
- m : n = 2 : 1
Substitute the values into the formula:

Hence proving the the location of point P on the coordinate plane is (2, 1).