# Position of points with respect to line :

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## Position of points with respect to line :

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

And points P(x₁ ,y₁) and Q(x , y) , 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 :

#### 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.

#### 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.

#### Origin side :

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

ax₁ + by₁ + c  and  c  have same sign.

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

ax₁ + by₁ + c  and  c  have opposite sign.

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