Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 148403 by Jonathanwaweh last updated on 27/Jul/21

Answered by Olaf_Thorendsen last updated on 27/Jul/21

$$\mathrm{Soit}\mathrm{G}\mathrm{un}\mathrm{point}\mathrm{du}\mathrm{plan}\mathrm{contenant}$$$$\mathrm{A}\mathrm{et}\mathrm{B}.\mathrm{Alors}\mathrm{G}\mathrm{est}\mathrm{le}\mathrm{barycentre}\mathrm{des}$$$$\mathrm{points}\mathrm{A}\mathrm{et}\mathrm{B}\mathrm{affecte}\mathrm{respectivement}$$$$\mathrm{des}\mathrm{coefficients}a\mathrm{et}b\mathrm{de}\mathrm{somme}\mathrm{non}$$$$\mathrm{nulle}a+b\ne 0\mathrm{si},\mathrm{par}\mathrm{definition}\mathrm{du}$$$$\mathrm{barycentre}:a\overrightarrow{\mathrm{GA}}+b\overrightarrow{\mathrm{GB}}=\overrightarrow{0}\left(1\right)$$$$$$$$\mathrm{Il}\mathrm{vient}\mathrm{que}\mathrm{les}\mathrm{vecteurs}\overrightarrow{\mathrm{GA}}\mathrm{et}\overrightarrow{\mathrm{GB}}$$$$\mathrm{sont}\mathrm{colineaires}\mathrm{et}\mathrm{donc}\mathrm{G}\mathrm{appartient}$$$$\mathrm{a}\mathrm{la}\mathrm{droite}\left(\mathrm{AB}\right).$$$$$$$$\mathrm{En}\mathrm{outre}\left(1\right)\mathrm{peut}{\mathrm{s}}^{\prime }\mathrm{ecrire}:$$$$\left(1\right):a\overrightarrow{\mathrm{GA}}+b(\overrightarrow{\mathrm{GA}}+\overrightarrow{\mathrm{AB}})=\overrightarrow{0}$$$$\overrightarrow{\mathrm{AG}}=\frac{b}{a+b}\overrightarrow{\mathrm{A}B}$$$$\mathrm{Si}a\mathrm{et}b\mathrm{sont}\mathrm{de}\mathrm{meme}\mathrm{signe},\mathrm{la}\mathrm{double}$$$$\mathrm{inegalite}0⩽\frac{b}{a+b}⩽1\mathrm{entraine}\mathrm{que}\mathrm{G}$$$$\mathrm{decrit}\mathrm{le}\mathrm{segment}\left[\mathrm{AB}\right].$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com