Position of points with respect to line :

Position of points with respect to line :

Let
Equation of a straight line –
ax + by + c = 0

And points P(x1,y1) and Q(x2 , y2) , then find position of points with respect to line-

Assume, the line PQ intersection point L at A(x, y) and let A divides PQ in the ratio m1:m2, then Position of points relative to a straight line :

position of points with respect to line

case 1:

If  ax1 + by1 + c = 0 and  ax2 + by2 + c = 0 both  has same sign then PQ is divided by straight line L  externally. And points lie on same side of a straight line ax + by + c = 0.

position of points with respect to line.

case2:

If ax1 + by1 + c = 0 and  ax2 + by2 + c = 0 both  has opposite sign then ,  PQ is divided by straight line L  internally.And points lie on opposite side of a straight line

ax + by + c = 0.

position of points with respect to line

Origin side :

    1. A point lies on origin side if and only if –

ax1 + by1 + c  and  c  have same sign.

position of points with respect to line.

2. A point lies on non- origin side if and only if –

ax1 + by1 + c  and  c  have opposite sign.