I have two points ( 0 , 0 ) and ( 93 , 3 )I'm trying to work out whether a point is on or below the line segment defined by those two point.Currently I'm using A x + B y + C = 0 to see if a point is on or below this line segment and this works correctly except for when the point is of the form ( 0 , y ) or ( x , 0 )What am I doing wrong? Do I need to use a different form of the linear equation?

Question

I have two points   (  0  ,  0  ) and   (  93  ,  3  )I&#039;m trying to work out whether a point is on or below the line segment defined by those two point.Currently I&#039;m using   A  x  +  B  y  +  C  =  0 to see if a point is on or below this line segment and this works correctly except for when the point is of the form   (  0  ,  y  ) or   (  x  ,  0  )What am I doing wrong? Do I need to use a different form of the linear equation?

Kroatujon3 · Accepted Answer

For this particular example it would seem to be easier to write the equation for the line in slope-intercept form:  y  =      1    31    x  +  0Then given any   (  x  ,  y  ), you can test directly whether the point lies above or below the point on the line that has the same   x coordinate.

delirija7z · Accepted Answer

Suppose your given points are   (      x    1    ,      y    1    ) and   (      x    2    ,      y    2    ). First get the slope   m  =                    y        1            −              y        2                            x        1            −              x        2            . The equation of the line joining the points is   y  −      y    1    =  m  (  x  −      x    1    ), where you just substitute       x    1    ,      y    1  , and   m. In slope intercept form the equation is  y  =  m  x  +  (      y    1    −  m      x    1    )  .Given a point   (  p  ,  q  ), first check that       x    1    ≤  p  ≤      x    2  . Then:   q  &amp;gt;  m  p  +  (      y    1    −  m      x    1    ) means the point is above the segment, and   q  &amp;lt;  m  p  +  (      y    1    −  m      x    1    ) means the point is below the segment.If you already have the equation of the line joining the points as   A  x  +  B  y  +  C  =  0, then the equation of the line can be expressed as   y  =  −      B    A    x  −      C    A  , so just check to see whether   q  &amp;gt;  −      B    A    p  −      C    A   or not.