Bonjour,
Soit DEF un triangle. Soit P et Q les points définis par :
DP = -3EF et DQ = 2/3EF
Montrer que les points D, P et Q sont alignés.

By: USER6585
27 Agustus 2025 mathematiques 5 minutes
4.5
163 views 163 comments 13 shares

Question

Grade: Education Subject: mathematiques
Bonjour,
Soit DEF un triangle. Soit P et Q les points définis par :
DP = -3EF et DQ = 2/3EF
Montrer que les points D, P et Q sont alignés.
Asked by:
163 Viewed 163 Answers

Answer (163)

Best Answer
(557)

Réponse :

Montrer que les points D; P et Q sont alignés

 vec(DP) = - 3vec(EF)  ⇔ vec(EF) = - 1/3vec(DP)

vec(DQ) = 2/3vec(EF)  ⇔ vec(EF) = 3/2vec(DQ)

donc - 1/3vec(DP) = 3/2vec(DQ)  ⇔ vec(DP) = - 9/2vec(DQ)

les vecteurs DP et DQ  sont colinéaires, car il existe un réel k = - 9/2 tel que vec(DP) = - 9/2vec(DQ)

On en déduit donc que les points D, P et Q sont alignés

Explications étape par étape :

Answered on 27 Agustus 2025

Related Articles

2n supra5 si n +3 supra 3

25 views 25 comments

cum fac reclama la prajitura Tiramisu?

38 views 38 comments

numeste 3 deformari ale coloanei vertebrale?Descrie una din ele (cauza,profilaxia,tratamentul)vaaaa rogg

104 views 104 comments

Treceti verbul DESCRIAU ,la diateza pasiva respecand modul.timpul , persoana si numarul... AJUTOOOORRR

103 views 103 comments

ABCD daca AD=6 cm .CD=7cm si m (D) =135

40 views 40 comments

pengertian trun in and folder on edmodo

39 views 39 comments

Suma a trei nr .este 624.Suma dintre primul si al treilea este 570.Al treilea nr.este o treime din al doilea nr.afla numerele

126 views 126 comments

Five mineral samples of equal mass of calcite, caco3 (mm 100.085) , had a total mass of 10.9 ± 0.1 g. what is the average mass of calcium in each sample? (assume that the relative uncertainties in atomic mass are small compared the uncertainty of the total mass.)

160 views 263 comments

If the 'ip2770' device is faulty, how can I confirm this?

57 views 57 comments

Fie unghiul AOB si BOC astfel incat masura unghiului AOB=64 de grade si masura unghiului BOC este drept
Sa se calculeze
măsura unghiului AOC
măsura unghiului DOE unde [OF si [OE sunt bisectoarele unghiului AOB si respectiv BOC

160 views 247 comments

What steps should I take to check the physical connection for the 'ip2770' device?

82 views 82 comments

Write a java class (mystackapp) to emulate a stack structure using an array. provide methods for push(), pop(), isempty(), peek(), and size(). use the postfix expression in the text (given below) to test your logic for evaluating the postfix form of the expression.. infix:: (3 * 4 - (2 + 5) ) * 4 / 2 postfix: 3 4 * 2 5 + - 4 * 2 / be sure to avoid error situations such as popping an empty stack, and the stack holding more than one item at the completion of the program. (note: you should pop() he

160 views 500 comments

o compunere de 8-10 randuri in care sa se afle toate cazurile substantivului cu articolul hotarat si nehotarat

110 views 110 comments

Va rog ajutati-ma ! Intr-un vas cu apa rece care are masa de 2 kg si temperatura de 10°C se introduce o bila fierbinte cu masa de 500g si temperatura de 90° C, din fier. Care va fi temperatura de echilibru?
Va rog ajutati-ma ca nu reusesc sa o rezolv..

160 views 266 comments

How did Comic Con Astana 2023 compare to other Comic Cons in the region?

72 views 72 comments

bonjour j'aimerais savoir comment sont les allemands a carnaval svp quelqu'un peux m'aider ?
merci d'avance :)

116 views 116 comments

tuliskan sepuluh persatuan?

27 views 27 comments

Bonjour, j'aimerai s'il vous plait que quelqu'un me corrige mon texte d'italien :

Parleremo di spazi e scambi. Le parole spazi e scambi coprono diverse realtà, presenteremo questa nozione dal punto di vista economico e umano. si puo avere domande come " perché gli italiani hanno molti stereotipi su essi ?" o "perché, c'è una fuga di cervelli tra i giovani" ? Ci aiutiamo di documenti per rispondere alle domande.
In primo documento vediamo un figlio con la sua madre, si occupa

160 views 500 comments