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Home Question Bank Math Geometry Archive 2024 November 19

Geometry Questions from Nov 19,2024

Browse the Geometry Q&A Archive for Nov 19,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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10) The equation of the horizontal line passing through the point \( (3,-5) \) is: \( \begin{array}{ll}\text { a) } x=3 & \text { b) } y=-3 \\ \text { c) } y=3 & \text { d) } x=5 \\ \text { e) None of the above } & \end{array} \) Soit ABCD un parallélogramme. I) On considère les points K et L tels que : \( \overrightarrow{D K}=\frac{5}{2} \overrightarrow{D A} \) et \( \overrightarrow{D L}=\frac{5}{3} \overrightarrow{D C} \) 1- Montrer que : \( \overrightarrow{B K}=\frac{3}{2} \overrightarrow{D A}-\overrightarrow{A B} \) et \( \overrightarrow{B L}=\frac{2}{3} \overrightarrow{D C}-\overrightarrow{B C} \) 2- a) Exprimer \( \overrightarrow{B K} \) et \( \overrightarrow{B L} \) en fonction de \( \overrightarrow{A B} \) et \( \overrightarrow{B C} \) b) Montrer que \( 2 \overrightarrow{B K}=-3 \overrightarrow{B L} \) c) Dédure que les points \( \mathrm{B}, \mathrm{K} \) et L sont alignés. II) 1 - Construire \( E, F, G \) et \( H \) tels que : \[ \overrightarrow{D E}=\frac{4}{3} \overrightarrow{D A} \text { et } \overrightarrow{B G}=\frac{4}{3} \overrightarrow{B C} \text { et } \overrightarrow{A F}=\frac{5}{4} \overrightarrow{A B} \quad \text { et } \overrightarrow{C H}=\frac{5}{4} \overrightarrow{C D} \] 2- Montrer que \( E F G H \) est un parallélogramme. III) Soit \( A B C \) un triangle. 1- Placer les points I et J tels que : \( \overrightarrow{A I}=\frac{1}{3} \overrightarrow{A B} \quad \) et \( \overrightarrow{A J}=3 \overrightarrow{A C} \) 2- Montrer que \( \overrightarrow{B J}=3 \overrightarrow{I C} \) 3- Déduire que \( (B J) \|(I C) \) 2) El radio de la circunferencia de longitud 10 Cm es: \( \begin{array}{llll}\text { a) } 2,23 \mathrm{Cm} & \text { b) } 1.59 \mathrm{Cm} & \text { c) } 1.64 \mathrm{Cm} & \text { d) } 1.6\end{array} \) 2. Dreptele \( a \) și \( b \) din figura alăturată sunt paralele. Valoarea lui \( x \) este egală cu: \( \begin{array}{ll}\text { a) } 59^{\circ} & \text { b) } 121^{\circ} \\ \text { c) } 131^{\circ} & \text { d) } 180^{\circ}\end{array} \) Exercice 57 : Soit \( A B C D \) un rectangle de centre \( O . E \) est le centre de gravité du triangle \( A B C \). 1. Construire le point \( F \) barycentre de \( (C ; 1) \) et \( (D ; 3) \). 2. Soit \( G \) le milieu du segment \( [E D] \). Montrer que \( G \) est le barycentre de \( (A ; 1) \); ( \( B ; 1) ;(C ; 1) \) et \( (D ; 3) \). 3. Montrer que \( G \) appartient à la droite \( (I F) \). 4. Soit \( K \) le point défini par : \( 4 \overrightarrow{A K}=3 \overrightarrow{A D} \). a) Déterminer deux réels \( a \) et \( b \) pour que \( K \) soit le barycentre de \( (A ; a) \) et ( \( D: b) \). b) Montrer que le milieu du segment \( [B C] \) ap- partient à la droite \( (G K) \). 5. a) Montrer que pour tout point \( M \) du plan, on a : \( 4 \overrightarrow{M A}-2 \overrightarrow{M B}-2 \overrightarrow{M D}=2 \overrightarrow{C A} \) b) Déterminer et construire l'ensemble des A line in a map represents a distance of 12 km . The line is 15 cm long. What is the scale of the map? \( \begin{array}{l}1: 100,000 \\ 1: 80,000 \\ 1: 60,000 \\ 1: 120,000\end{array} \) The height of a tower is shown as 25 mm in a drawing. The actual height is 20 m . What is the scale of the drawing? 1:250 1:800 \( 1: 500 \) \( 1: 400 \) Бічне ребро похилої призми дорівнюе \( 4 \sqrt{3} \) см і утворюе з площиною основи кут \( 60^{\circ} \). Знайдіть висоту похилої призми. A model of a car has a height of 10 cm . The actual car height is 1 m. What is the scale of the model? 1:5 1:100 1:10 1:50 A map has a scale of \( 10 \mathrm{~mm}: 2 \mathrm{~m} \). Express this ratio in the form \( 1: k \). \( \begin{array}{l}1: 200 \\ 1: 20 \\ 1: 100 \\ 1: 50\end{array} \)
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