Question-226622

Question Number 226622 by fantastic2 last updated on 07/Dec/25

Commented by mr W last updated on 07/Dec/25

λ=(m/n)=((x−x_1 )/(x_2 −x))=((y−y_1 )/(y_2 −y)) if λ<0, there are only two cases: x−x_1 >0, x_2 −x<0 ⇒x>max(x_1 ,x_2 ) x−x_1 <0, x_2 −x>0 ⇒x>min(x_1 ,x_2 ) that means (x, y) lies outside the segment from (x_1 ,y_1 ) to (x_2 ,y_2 ).

$$\lambda=\frac{{m}}{{n}}=\frac{{x}−{x}_{\mathrm{1}} }{{x}_{\mathrm{2}} −{x}}=\frac{{y}−{y}_{\mathrm{1}} }{{y}_{\mathrm{2}} −{y}} \\ $$$${if}\:\lambda<\mathrm{0},\:{there}\:{are}\:{only}\:{two}\:{cases}: \\ $$$${x}−{x}_{\mathrm{1}} >\mathrm{0},\:{x}_{\mathrm{2}} −{x}<\mathrm{0}\:\Rightarrow{x}>{max}\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} \right) \\ $$$${x}−{x}_{\mathrm{1}} <\mathrm{0},\:{x}_{\mathrm{2}} −{x}>\mathrm{0}\:\Rightarrow{x}>{min}\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} \right) \\ $$$${that}\:{means}\:\left({x},\:{y}\right)\:{lies}\:{outside}\:{the} \\ $$$${segment}\:{from}\:\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} \right)\:{to}\:\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} \right). \\ $$

Commented by fantastic2 last updated on 07/Dec/25

$${thank}\:{you} \\ $$

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Question-226622

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