Question

Position of two points relative to a given line.

Answer 1

Let the line be L =ax+by+c=0

P(x₁ ,y₁) and A(x₂ ,y₂) are two given points.

i. If ax₁ +by₁ +c and ax₂ +by₂ +c both are of the same sign and hence \(\cfrac{ax_1+by_1+c}{ax_2+by_2+c}>0\) then the points P and Q lie on same side of line ax+by+c=0

ii. If ax₁ +by₁ +c and ax₂ +by₂ +c are of opposite sign and hence

\(\cfrac{ax_1+by_1+c}{ax_2+by_2+c}<0\)

points P and Q lie on opposite side of the line ax+by+c=0

iii. If origin lie on line then the line is know as origin side

iv.  A point (x₁ y₁) will lie on origin side of the line ax+by+c=0 if ax₁ +by₁ +c and c have same sign.

v.  A point (x₁, y₁) will lie on non-origin side of the line ax+by+c=0 if ax₁ +by₁ +c and c have opposite sign