Grade 10 / vectors and coordinates 53 exercises (including 45 corrected)

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Quaid’OrientQuaid’OrientruedeTunisruedeTunisruedeFondèrerueLazareCarnotrueLazareCarnotQuaiRhinetDanubeQuaiRhinetDanubePontdepierreQuaiLouisPasterAvenueVictorHugoQuaiAdolpheMerleQuaiLouisPasterRuedeLonguyonQuaideBoscQuaidelaRésistanceQuaidelaRésistanceRueMontmorencyRueMontmorencyBoulevardDanielleCasanovaRuedesJardinsRueduDéputéMolleRueduLucienSaletteRueAragoRuedelaLibertéRueMercierRueHenriBarbusseRueHenriBarbusseRued’IssankaRuedel’EgalitéRueGeorgesBrassensRueduGénéraldeGaulleRueduMaireAussenacRueduDéputéSalisRuedelaFédérationRuedelaRévolutionRuedelaCaraussaneImpasseParmentierRuedu8Mai1945RueGambettaRued’AlsaceLorraineRueduGénéraLeclercRueTissier-PonsRueduColonelFabienRueRaymondLefebreRuedeBelfortPassageLeDauphinGalerieGambettaRueFrédéricMistral654321ABCDEFGHIJK 12345678910ABCDEFG75-5312-211212584233-6-5435-5139 ChingQuizz : 8 exercises available for Quizz assessment : 1. Tracking E.490 Here is a map of the historic center of Sète, a city in southern France. Use the map to answer the questions : 1 How can you indicate the location of the street ˇ du 8 mai 1945 ı on this map? 2 How would you indicate the location of the ˇ de la République ı? 3 quay? Given that the ˇ de la République ı quay measures 350 meters, give the scale of this map. E.492 1 Tick boxes E7 and B10 . 2 Knowing that an empty square has a zero value, calculate the value of the following two formulas : a A : =B3+C1+F2+E5 b B : =A7+D10+D9+F4-C5 3 A cell range is a set of cells expressed in the form ˇ C3:F5 ı designating all the cells contained in the rectangle having as opposite vertices the cells C3 and F5 . Circle this range of cells. 4 The functions SUM(...) and AVERAGE(...) respectively calculate the sum and average of the values of the cells passed as arguments. Give the value of the following formulas : a SOMME(C3:F5) b SOMME(C1:C10) c MOYENNE(A3:F4) d SOMME(C1:C9)+SOMME(C5:G5) https://chingmath.fr chapExoCorrec/490 sacados/490 Quaid’OrientQuaid’OrientruedeTunisruedeTunisruedeFondèrerueLazareCarnotrueLazareCarnotQuaiRhinetDanubeQuaiRhinetDanubePontdepierreQuaiLouisPasterAvenueVictorHugoQuaiAdolpheMerleQuaiLouisPasterRuedeLonguyonQuaideBoscQuaidelaRésistanceQuaidelaRésistanceRueMontmorencyRueMontmorencyBoulevardDanielleCasanovaRuedesJardinsRueduDéputéMolleRueduLucienSaletteRueAragoRuedelaLibertéRueMercierRueHenriBarbusseRueHenriBarbusseRued’IssankaRuedel’EgalitéRueGeorgesBrassensRueduGénéraldeGaulleRueduMaireAussenacRueduDéputéSalisRuedelaFédérationRuedelaRévolutionRuedelaCaraussaneImpasseParmentierRuedu8Mai1945RueGambettaRued’AlsaceLorraineRueduGénéraLeclercRueTissier-PonsRueduColonelFabienRueRaymondLefebreRuedeBelfortPassageLeDauphinGalerieGambettaRueFrédéricMistral654321ABCDEFGHIJK chapExoCorrec/492 sacados/492 12345678910ABCDEFG75-5312-211212584233-6-5435-5139
xxyy-4-3-2-1234I-4-3-2-123JO -2-2-1-1IJ223344OABC 011xyAB E.6472 Consider the plane provided with an O ; I ; J orthonormal coordinate system shown below : 1 a Place points : A − 7 2 ; 1 ; B 2 ; − 1 2 ; C 1 ; − 7 2 b Draw the triangle ABC . 2 a Place points : D 3 ; 1 2 ; E 1 2 ; 9 4 ; F − 3 4 ; − 13 4 b Draw the triangle DEF . E.8036 Consider the reference frame O ; I ; J any shown below and the three points A , B , C : 1 Give the coordinates of the points A , B , C . 2 Place points D and E with coordinates : D (2 ; 1) ; E ( − 1 ; − 2) E.6470 Consider the plane provided with a reference frame O ; I ; J . Say whether the following assertions are true or false : 1 Let A and B be two points with the same abscissas. The line ( AB ) is parallel to the abscissa axis. 2 Let A and B be two points with the same abscissas. The line ( AB ) is parallel to the ordinate axis. 3 triangle OIJ is a right-isosceles triangle. 4 The two points A (3 ; 2) and B (3 ; − 2) are symmetrical with respect to the x-axis. 5 The two points A (1 ; 2) and B ( − 1 ; − 2) are symmetrical with respect to the origin of the reference frame. E.11811 On considère le plan muni d’un repère O ; I ; J orthonormé représenté ci-dessous : 1 a Placer les points : A − 7 2 ; 1 ; B 2 ; − 1 2 ; C 1 ; − 7 2 b Tracer le triangle ABC . 2 a Placer les points : D 3 ; 1 2 ; E 1 2 ; 9 4 ; F − 3 4 ; − 13 4 b Tracer le triangle DEF . 2. Reminders about the reference point on the plan E.11272 In the coordinate plane, consider the segment [ AB ] shown below : https://chingmath.fr chapExoCorrec/6472 sacados/6472 xxyy-4-3-2-1234I-4-3-2-123JO chapExoCorrec/8036 sacados/8036 -2-2-1-1IJ223344OABC chapExoCorrec/6470 sacados/6470 chapExoCorrec/11811 sacados/11811 xxyy-4-3-2-1234I-4-3-2-123JO chapExoCorrec/11272 sacados/11272 011xyAB
011xyAB 011xyAB 011xyAB 011xyAB(d -4-3-2-1234I-123JOABC 1 Let [ A B ] be the image of the segment [ AB ] under the rotation with center O and angle 90 o clockwise. Represent the segment [ A B ] in the coordinate system above. 2 Give the coordinates of the points A and B . E.11273 In the coordinate plane, consider the segment [ AB ] shown below : 1 Let [ A B ] be the image of the segment [ AB ] under the rotation with center O and angle 90 o clockwise. Represent the segment [ A B ] in the coordinate system above. 2 Give the coordinates of the points A and B . E.11274 In the plane with coordinates : 1 Give the coordinates of points A and B . 2 a Place points A and B as images of points A and B by symmetry about the y-axis. We will also draw the segment [ A B ] . b Give the coordinates of points A and B . E.11276 In the plane with coordinates : 1 Give the coordinates of points A and B . 2 a Draw the segment [ A B ] , which is the image of the segment [ AB ] under the symmetry with center O (0 ; 0) . b Give the coordinates of points A and B . E.11275 In the plane with coordinates : 1 Give the coordinates of points A and B . 2 a Place points A and B as images of the endpoints of segment [ AB ] by symmetry about axis ( d ) . b Give the coordinates of points A and B . 3. Introduction to Vector Coordinates E.11743 Dans le plan muni d’un repère O ; I ; J , on considère les trois points A , B et C : 1 Donner les coordonnées des trois points. 2 a En partant de A , de combien faut-il se déplacer suiv-ant l’axe des abscisses et suivant l’axe des ordonnées pour arriver au point B ? b Même question pour un déplacement de A vers le point C ? https://chingmath.fr chapExoCorrec/11273 sacados/11273 011xyAB chapExoCorrec/11274 sacados/11274 011xyAB chapExoCorrec/11276 sacados/11276 011xyAB chapExoCorrec/11275 sacados/11275 011xyAB(d sacados/11743 -4-3-2-1234I-123JOABC
-3-2-123I-1JOCDAB -6-4-2246I-4-224JOABCDEFGHKL -22I2JOABCDEF -8-7-6-5-4-3-2-1234567I-4-3-2-12345JOA1B1A2B2A3B3A4B4 -4-224I2JOABCDEF E.11812 Dans le plan muni d’un repère O ; I ; ; J , on considère les quatre points A , B , C , D : 1 Donner les coordonnées de ces quatre points. 2 a Montrer que le déplacement du point A vers le point B a pour valeur 5 3 en abscisses et pour valeur − 2 en ordonnées. b Donner les valeurs caractérisant le déplacement du point C vers le point D ? E.11813 Dans le plan muni d’un repère O ; I ; ; J , on considère les quatre points A , B , C , D : 1 Donner les coordonnées de ces quatre points. 2 a Montrer que le déplacement du point A vers le point B a pour valeur 5 3 en abscisses et pour valeur − 2 en ordonnées. b Donner les valeurs caractérisant le déplacement du point C vers le point D ? 4. Graphical reading of vector coordinates E.11293 Equip the plane with the orthonor-mal reference frame O ; I ; J : 1 Graphically, verify the coordinates of the two vectors : −−→ AB (1 ; 4) ; −−→ CD (5 ; − 2) 2 Graphically, give the coordinates of the vectors −−→ EF , −−→ GH , ~ KL . E.11294 Equip the plane with the orthonor-mal reference frame O ; I ; J : Graphically, determine the coordinates of the vectors : −−→ AB ; −−→ CD ; −−→ EF . E.939 In the orthonormal coordinate system ( O ; I ; J ) shown below, four vectors are depicted : Determine the coordinates of these four vectors graphically. E.11854 On munit le plan du repère O ; I ; J orthonormé : Graphiquement, déterminer les coordonnées des vecteurs : −−→ AB ; −−→ CD ; −−→ EF . https://chingmath.fr sacados/11812 -3-2-123I-1JOCDAB sacados/11813 -3-2-123I-1JOCDAB chapExoCorrec/11293 sacados/11293 -6-4-2246I-4-224JOABCDEFGHKL chapExoCorrec/11294 sacados/11294 -22I2JOABCDEF chapExoCorrec/939 sacados/939 -8-7-6-5-4-3-2-1234567I-4-3-2-12345JOA1B1A2B2A3B3A4B4 chapExoCorrec/11854 sacados/11854 -4-224I2JOABCDEF
-2-123456I-1JOABCD A1B1A2B2A3B3-4-3-2-1234I-4-3-2-1234JO -6-4-2246I-4-224JOABCDEFGHKLMN E.11867 On munit le plan du repère O ; I ; J orthonormé : Graphiquement, déterminer les coordonnées des vecteurs : −−→ AB ; −−→ CD 5. Coordinates of vectors E.2057 Consider the orthonormal coordi-nate system ( O ; I ; J ) and the three vectors shown below : 1 Graphically, give the coordinates of the three vectors −−−→ A 1 B 1 , −−−→ A 2 B 2 , −−−→ A 3 B 3 . 2 Complete the following table : i ( x A i ; y A i ) ( x B i ; y B i ) x B i − x A i y B i − y A i 1 2 3 Proposition: In the plane equipped with a coordinate sys-tem, consider the two points A ( x A ; y A ) and B ( x B ; y B ) . The coordinates of vector −−→ AB are: −−→ AB ( x B − x A ; y B − y A ) 3 Check that you obtain the same coordinates using the above calculation. E.2062 1 Graphically, determine the coordinates of the vectors −−→ AB , −−→ CD and −−→ EF . 2 a Give the coordinates of points G , H , K , L , M and N . b Deduce, by calculation, the coordinates of the vectors −−→ GH , −−→ KL and −−→ MN . https://chingmath.fr chapExoCorrec/11867 sacados/11867 -2-123456I-1JOABCD chapExoCorrec/2057 sacados/2057 A1B1A2B2A3B3-4-3-2-1234I-4-3-2-1234JO chapExoCorrec/2062 sacados/2062 -6-4-2246I-4-224JOABCDEFGHKLMN
-5-4-3-2-1234I-3-2-12345JO -4-3-2-123456I-123JO E.940 Consider a plane equipped with an orthonormal coordinate system O ; I ; J ) . Consider the fol-lowing four points, whose coordinates are given : A (3 ; 2) ; B ( − 1 ; 4) ; C ( − 4 ; 0) ; D (0 ; − 2) 1 By calculation : a Determine the coordinates of the vectors −−→ AB and −−→ DC . b What can be said about the vectors −−→ AB and −−→ DC ? Jus-tify your answer. c What type of quadrilateral is ABCD ? 2 Observe: In the coordinate system below, plot the four points and verify the results of question 1 . E.11855 Dans le plan muni d’un repère, on con- sidère les quatre points : A ( − 2 ; 3) ; B (1 ; 2) ; C (5 ; − 1) ; D ( − 1 ; 2) 1 Déterminer les coordonnées des vecteurs −−→ AB et −−→ CD . 2 Dans le repère O ; I ; J : a Placer ces quatre points. b Vérifier graphiquement les réponses à la question 1 . E.11856 Dans le plan muni d’un repère, on con-sidère les quatre points : A (5 ; − 3) ; B (4 ; 1) ; C ( − 1 ; 3) ; D ( − 2 ; − 2) Déterminer les coordonnées des vecteurs −−→ AB et −−→ CD . E.11857 Dans le plan muni d’un repère, on con-sidère les quatre points : A ( − 3 ; 5 ; 1) ; B (1 ; − 1 ; 5) ; C (5 ; − 2 ; 5) ; D (4 ; − 0 ; 5) Déterminer les coordonnées des vecteurs −−→ AB et −−→ CD . E.11868 Dans le plan muni d’un repère, on con-sidère les quatre points : A (5 ; − 1) ; B ( − 4 ; − 5) ; C ( − 2 ; 5 ; 3) ; D (3 ; − 2 ; 5) Déterminer les coordonnées des vecteurs −−→ AB et −−→ CD . 6. Spotted geometry E.8316 Consider the plane equipped with a coordinate system O ; I ; J and the points A and B with coordinates : A ( − 4 ; − 2) ; B (3 ; − 4) 1 Establish that : −−→ AB (7 ; − 2) . 2 Consider the two points C and D with coordinates : C (1 ; 1) ; D (8 ; − 1) a Determine the coordinates of vector −−→ CD . b Name the parallelogram formed by the four points A , B , C , and D . 3 Without justification, give the coordinates of the point E such that the quadrilateral ABCE is a parallelogram. E.11405 In the plane equipped with a coor-dinate system, consider the four points : A ( − 3 ; 2) ; B (1 ; 5) ; C (6 ; 0) ; D (2 ; − 3) 1 Justify that −−→ AB (4 ; 3) . 2 a Determine the coordinates of vector −−→ DC . b Justify that ABCD is a parallelogram. https://chingmath.fr chapExoCorrec/940 sacados/940 -5-4-3-2-1234I-3-2-12345JO chapExoCorrec/11855 sacados/11855 -4-3-2-123456I-123JO chapExoCorrec/11856 sacados/11856 chapExoCorrec/11857 sacados/11857 chapExoCorrec/11868 sacados/11868 chapExoCorrec/8316 sacados/8316 chapExoCorrec/11405 sacados/11405
-4-3-2-1234I-2-12JOABD -4-3-2-1234567I-2-123456JOEFGHL E.9583 In the plane provided with a refer-ence frame O ; I ; J orthonormal, consider the three corners A , B , D shown below : 1 a Determine the coordinates of the vector −−→ AB . b Knowing that the point C has coordinates C (6.5 ; 0.5) , demonstrate that the quadrilateral ABCD is a paral-lelogram. 2 Give, without justification, the coordinates of the point E such that ABDE is a parallelogram. E.11336 In the plane with a coordinate sys-tem, consider the four points : P (1 ; 5 ; 3 ; 2) ; Q ( − 2 ; 3 ; 0 ; 8) ; R (4 ; 3 ; − 2 ; 4) ; S ( − 5 ; 1 ; 6 ; 4) 1 Determine the coordinates of vectors −→ PR and −→ SQ . 2 Justify that these four points form a parallelogram. Name this quadrilateral. E.8293 In an orthonormal coordinate system ( O ; I ; J ) , consider the following four points characterized by their coordinates : A (2 ; 2) ; B ( − 0 ; 5 ; − 1) ; C ( − 2 ; 0 ; 5) ; D (0 ; 5 ; 3 ; 5) 1 Justify that −−→ AB ( − 2 ; 5 ; − 3) 2 Justify that the quadrilateral ABCD is a parallelogram. E.919 Equip the plane with an or-thonormal coordinate system ( O ; I ; J ) and consider the five points shown below : 1 Graphically, determine the coordinates of points E , F , G , H , L . 2 a Determine, by calculation, the coordinates of the vectors −→ FL and −−→ HG . b Deduce the nature of FLGH . 3 a Determine, by calculation, the coordinates of vector −−→ EF . b Justify that quadrilateral EFGH is a parallelogram. 4 Specify the position of F on the segment [ EL ] . Justify your answer. 5 Copy and complete the equation : −→ FL + −−→ EH = −→ ::: E.938 In a plane with an orthonormal coordinate system ( O ; I ; J ) , where the unit of measurement is the centimeter, consider the points : A ( − 3 ; 0) ; B (1 ; 4) ; C (5 ; 3) ; D (1 ; − 1) 1 Construct this coordinate system and plot the points A , B , C , and D . 2 Calculate the coordinates of the vectors −−→ AB and −−→ DC . 3 What can we deduce about the nature of quadrilateral ABCD ? For the rest of this section, this quadrilateral ABCD is called figure 1. 4 Construct figure 2. , the image of figure 1. under the symmetry with center B . 5 Construct figure 3. , the image of figure 1. under the symmetry with axis ( CD ) . 6 a Construct the figure 4. , which is the image of the figure 1. under the vector translation −→ AC . b What other transformation allows us to go from the figure 1. to the figure 4. ? E.498 In an orthonormal coordinate system ( O ; I ; J ) , consider the following four points, characterized by their coordinates : A 5 3 ; 7 4 ; B 11 3 ; − 5 4 ; C 16 7 ; 12 5 ; D 2 7 ; 27 5 Prove that the quadrilateral ABCD is a parallelogram. E.6487 In an orthonormal frame of reference ( O ; I ; J ) , consider the following four points characterized by their coordinates : A 4 3 ; − 1 4 ; B − 7 3 ; 1 8 ; C 5 6 ; 1 2 ; D 9 2 ; 1 8 Justify that the quadrilateral ABCD is a parallelogram. E.9699 In the plane provided with an or-thonormal reference frame, consider the points : A 1 2 ; − 3 2 ; B ( − 2 ; 0) ; C − 1 3 ; 15 7 ; D 13 6 ; 9 14 Establish that the quadrilateral ABCD is a parallelogram. E.11871 Dans le plan muni d’un repère, on con-sidère les points : A ( − 3 ; 5 ; 6) ; B (1 ; 5 ; 2 ; 5) ; C ( − 2 ; 5 ; − 6 ; 5) ; D ( − 7 ; 5 ; − 3) 1 Déterminer les coordonnées des vecteurs −−→ AB et −−→ DC . 2 a Quelle relation vectorielle, la question 1 , permet-elle d’affirmer? b Nommer le parallélogramme obtenu à l’aide de ces qua-tre points? https://chingmath.fr chapExoCorrec/9583 sacados/9583 -4-3-2-1234I-2-12JOABD chapExoCorrec/11336 sacados/11336 chapExoCorrec/8293 sacados/8293 chapExoCorrec/919 sacados/919 -4-3-2-1234567I-2-123456JOEFGHL chapExoCorrec/938 sacados/938 chapExoCorrec/498 sacados/498 chapExoCorrec/6487 sacados/6487 chapExoCorrec/9699 sacados/9699 chapExoCorrec/11871 sacados/11871
-5-4-3-2-12345I-123JO -4-22468I-6-4-224JO 7. Search for the coordinates of a point E.8297 Consider the plane equipped with a coordinate system O ; I ; J and the three points A , B , C with coordinates : A ( − 2 ; − 1) ; B (2 ; 1) ; C ( − 1 ; 1) 1 Place points A and B in the coordinate system below : 2 Without justification, give the coordinates of point D such that : −−→ AB = −−→ CD Proposition: Consider A ( x A ; y A ) and B ( x B ; y B ) , two points in the marked plane. The vector −−→ AB has the following coor-dinates : −−→ AB ( x B − x A ; y B − y A ) Two vectors are equal if and only if they have the same coordinates. 3 Using the coordinates of these four points, verify that the two vectors −−→ AB and −−→ CD are equal. Proposition: ABCD is a parallelogram if and only if −−→ AB = −−→ DC 4 Name the parallelogram formed by these four points. E.2774 The plane is equipped with an or-thonormal reference frame O ; I ; J : Consider the three points A , B , C with respective coordinates (2 ; − 2) , ( − 3 ; 4) , (2 ; 1) . 1 Determine the coordinates of vector −−→ AB . 2 Consider the point D such that the quadrilateral ABCD is a parallelogram; let ( x D ; y D ) be the coordinates of the point D . a Justify that the coordinates of point D satisfy the fol-lowing two equalities: 2 − x D = − 5 ; 1 − y D = 6 b Deduce the coordinates of point D . E.920 In an orthonormal coordinate sys-tem ( O ; I ; J ) , consider the points : A (1 ; 2) ; B ( − 1 ; 4) ; C ( − 2 ; 1) Consider a point K such that ACBK is a parallelogram: 1 Give a vector relation characterizing the point K . 2 Determine the coordinates of the point K . https://chingmath.fr chapExoCorrec/8297 sacados/8297 -5-4-3-2-12345I-123JO chapExoCorrec/2774 sacados/2774 -4-22468I-6-4-224JO chapExoCorrec/920 sacados/920
-5-4-3-2-12345I-2-12JO -6-5-4-3-2-123I-3-2-1234JO E.11316 Consider the plane equipped with a coordinate system O ; I ; J and the three points A and B with coordinates : A ( − 2 ; − 1) ; B (2 ; 1) ; C (4 ; 0 ; 5) 1 Place the points A , B , C in the coordinate system below : 2 a Determine the coordinates of vector −−→ AB . b Determine the coordinates of point D such that ABCD is a parallelogram. c Place point D on the coordinate plane and draw quadrilateral ABCD . E.949 In an orthonormal coordinate system O ; I ; J where the unit of measurement is the centimeter. Consider the following three points : A (2 ; 1) ; B ( − 3 ; 3) ; C (0 ; − 2) 1 Plot the points A , B , and C . 2 Calculate the coordinates of vector −−→ AB . 3 a Determine the coordinates of point M so that quadrilateral ABMC is a parallelogram. b Draw parallelogram ABMC . E.521 We mark the plane with a reference point ( O ; I ; J ) . Let A (3 ; 1) , B (5 ; − 2) , and C ( − 1 ; 0) be three points in the plane. 1 Find the coordinates of the vector −−→ AB . 2 Let D be a point in the plane that satisfies the equation : −−→ CD = −−→ AB Find the coordinates of the point D . E.11406 In the plane equipped with a coor-dinate system, consider the three points : M (2 ; 8 ; 1 ; 3) ; N (5 ; 4 ; − 1 ; 2) ; P ( − 0 ; 7 ; − 1 ; 6) 1 Determine the coordinates of vector −−→ MN . 2 Determine the coordinates of point Q such that MNPQ is a parallelogram. E.11337 In the plane marked with a refer-ence point O ; I ; J , consider the following three points : K (2 ; 7 ; − 0 ; 6) ; L ( − 0 ; 3 ; 1 ; 9) ; M (4 ; 2 ; 2 ; 3) Determine the coordinates of point N such that quadrilateral KLMN is a parallelogram. E.8119 In the plane marked with a reference point O ; I ; J , consider the following three points : A ( − 2 ; 3) ; B (3 ; 1) ; C ( − 1 ; 2) Determine the coordinates of point D such that quadrilateral ABCD is a parallelogram. E.9581 In the plane provided with a refer-ence frame O ; I ; J , consider the following three points : A ( − 1.8 ; 2.5) ; B (3.2 ; 0.9) ; C ( − 1 ; 1.4) Determine the coordinates of the point D such that the quadrilateral ABCD is a parallelogram. E.11614 Mark the plane with a refer-ence point ( O ; I ; J ) . Let E (12 ; 1 ; 34) , F (25 ; 4 ; 10 ; 5) , and G (30 ; − 2) be the coordinates. Determine the coordinates of point H so that quadrilateral EFGH is a parallelogram. E.8124 Consider the three points A , B , C of coordinates : A 1 2 ; 1 4 ; B 16 3 ; − 15 4 ; C − 1 ; 1 3 Determine the coordinates of the point D such that the quadrilateral ABCD is a parallelogram. E.8120 In the plane provided with a refer-ence frame O ; I ; J , consider the following three points : A − 1 3 ; 3 5 ; B 7 2 ; − 2 5 ; C − 5 3 ; 2 Determine the coordinates of the point D such that the quadrilateral ABCD is a parallelogram. E.11339 Let x be a real number. Consider the four points in the plane : P (2 x +3 ; 5 − 2 x ) ; Q ( x +1 ; 2+ x ) R (3 − 2 x ; 3 x +1) ; S ( x − 2 ; 2 x +1) Determine the value of x so that the quadrilateral PQSR is a parallelogram. https://chingmath.fr chapExoCorrec/11316 sacados/11316 -5-4-3-2-12345I-2-12JO chapExoCorrec/949 sacados/949 -6-5-4-3-2-123I-3-2-1234JO chapExoCorrec/521 sacados/521 chapExoCorrec/11406 sacados/11406 chapExoCorrec/11337 sacados/11337 chapExoCorrec/8119 sacados/8119 chapExoCorrec/9581 sacados/9581 chapExoCorrec/11614 sacados/11614 chapExoCorrec/8124 sacados/8124 chapExoCorrec/8120 sacados/8120 chapExoCorrec/11339 sacados/11339
-4-3-2-123456789I-5-4-3-2-1234JO E.11869 Dans le plan muni d’un repère, on con-sidère les trois points : A (7 ; 1) ; B ( − 3 ; − 4) ; C ( − 2 ; − 2) 1 a Justifier que les coordonnées du vecteur −−→ AB − 2 − 2 . b Déterminer les coordonnées du point D tel que ABCD soit un parallélogramme. 2 Dans le repère O ; I ; J , placer ces quatre points : E.11872 Dans le plan muni d’un repère, on con-sidère le parallélogramme ABCD . On a les coordonnées : A ( − 5 ; 6) ; C (17 ; − 5) Les points B et D ont la même abscisse. Le point B a pour ordonné 3 . Déterminer les coordonnées des points B et D . Indication : toute trace de recherche même incomplète sera prise en compte dans l’évaluation. https://chingmath.fr chapExoCorrec/11869 sacados/11869 -4-3-2-123456789I-5-4-3-2-1234JO chapExoCorrec/11872 sacados/11872