Determine if the line passes through the area of the rectangle

Questions
,
1

How can I do the calculation to know if the line is passing through the rectangle (obstacle), since I only know the position of sta1 and sta2 and I also know the x_min, x_max and y_min, y_max of the rectangle?

Capturadetelade2022-11-2514-35-22.png
Capturadetelade2022-11-2514-35-22.png289×282 6.78 KB

sta1 position(x,y) = (1,5) sta2 position(x,y) = (5,1)

retangle x_min = 3 retangle x_max = 4 retangle y_min = 2 retangle y_max = 3

2

Hint

FindInstance[y==-1*x+6&&3<=x<=4&&2<=y<=3,{x,y}]

returns

{{x->4,y->2}}

and

FindInstance[y==-1*x+8&&3<=x<=4&&2<=y<=3,{x,y}]

returns

{}

Can you construct the input needed by Findinstance from the information you have about the points and test whether the result returned from FindInstance is an empty list or not?