$$\mathbf{P} = \mathbf{P}_1 + \left( \mathbf{P}_2 - \mathbf{P}_1 \right) \; t = \mathbf{P}_1 + \mathbf{v} \; t $$

in cui

$$0 \le t \le 1 $$

Riferendosi alle singole coordinate

$$x = x_1 + \left( x_2 - x_1 \right) \; t$$

$$y = y_1 + \left( y_2 - y_1 \right) \; t$$