[tex]\text{Stabiliti daca punctele:} \;\;A(-2; 10), \;\;B(4; -5),\;\;C(2,0) \;\;\;sunt\;coliniare. \\ Rezolvare: \\ \text{Calculam distantele dintre puncte.} \\ \text{Comparam suma distantelor mai mici cu distanta cea mai mare.} \\ \\ dAB = \sqrt{ (xA-xB)^{2}+ (yA-yB)^{2} }= \\ = \sqrt{ (-2-4)^{2}+ (10+5)^{2}}= \\ =\sqrt{ (-6)^{2}+ (15)^{2}}=\sqrt{ 36+ 225}=\sqrt{ 261}=3 \sqrt{29} [/tex]
[tex]dBC= \sqrt{ (xB-xC)^{2}+ (yB-yC)^{2} }= \\ = \sqrt{ (4-2)^{2}+ (-5-0)^{2}}= \\ =\sqrt{ (2)^{2}+ (-5)^{2}}=\sqrt{ 4+25}=\sqrt{ 29} \\ \\ dAC= \sqrt{ (xA-xC)^{2}+ (yA-yC)^{2} }= \\ = \sqrt{ (-2-2)^{2}+ (10-0)^{2}}= \\ =\sqrt{ (-4)^{2}+(10)^{2}}=\sqrt{ 16+100}=\sqrt{116}=2 \sqrt{29} \\ \\dBC+dAC = \sqrt{ 29}+2\sqrt{ 29} = 3\sqrt{ 29} = dAB \\=> \text{ Punctele A, B, C sunt coliniare si C este intre A si B}[/tex]
