Calculate point P on AB¯¯¯¯¯¯¯¯ such that the ratio of AP to PB is 1:3.
Let's assume that point A has coordinates (x1, y1) and point B has coordinates (x2, y2).
The coordinates of point P can be calculated using the ratio of AP to PB, which is 1:3.
Let's consider the x-coordinate of point P.
The difference between the x-coordinates of A and B is: Δx = x2 - x1
Since AP to PB is 1:3, the difference between the x-coordinate of P and A is: Δx_AP = Δx / 4
Thus, the x-coordinate of point P is: xP = x1 + Δx_AP
Similarly, we can calculate the y-coordinate of point P.
The difference between the y-coordinates of A and B is: Δy = y2 - y1
Since AP to PB is 1:3, the difference between the y-coordinate of P and A is: Δy_AP = Δy / 4
Thus, the y-coordinate of point P is: yP = y1 + Δy_AP
Therefore, the coordinates of point P are: (xP, yP) = (x1 + Δx_AP, y1 + Δy_AP)