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 :
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 :
- 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.
