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Home Question Bank Math Geometry Archive 2024 December 06

Geometry Questions from Dec 06,2024

Browse the Geometry Q&A Archive for Dec 06,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Be sure to remember solid vs, dashed lines, 2 Trace la droite représentant la relation \( 2 x+3 y=6 \). Si cette droite coupe l'axe des \( x \) au point A et l'axe des y au point \( B \), calcule l'aire du triangle OAB où \( O \) est le point d'origine. 17. Rotate the figure below \( 270^{\circ} \). Which Quadrant will the image (Page 47-50, 55-56) (1pt) cuadrante estará la imagen? (Page \( \begin{array}{ll}\text { A. Quadrant } 1 & \text { B. Quadrant } 2 \\ \text { C. Quadrant } 3 & \text { D. Quadrant } 4\end{array} \) 4. Fie \( u=(-1,8,2), w=(7,4,-5) \) din \( \mathbf{R}^{3} \) şi subspaţiile \( S_{1}=\left\{\left(x_{1}, x_{2}, x_{3}\right) \in \mathbf{R}^{3} \mid x_{1}+2 x_{2}+3 x_{3}=0\right\} \), \( S_{2}=\{(a, 2 b, 2 a+b) \mid a, b \in \mathbf{R}\}, S_{3}=S p\{w\} \), subspaţiul lui \( \mathbf{R}^{3} \) generat de \( w \). i) Să se arate că \( u \in S_{2} \) şi \( u \notin S_{1} \). ii) Să se determine dimensiunile subspaţiilor \( S_{1}, S_{2}, S_{3} \), indicând câte o bază în fiecare. iii) Să se determine \( S_{1}+S_{2} \) şi \( S_{1}+S_{3} \). Sunt aceste sume directe? (Justificați!) iv) Să se interpreteze geometric \( S_{1}, S_{2}, S_{3}, S_{1}+S_{2}, S_{1}+S_{3} \) şi \( \left(S_{1}+S_{2}\right) \cap\left(S_{1}+S_{3}\right) \). v) Să se calculeze \( \|u\| \) şi \( \langle u, w\rangle \) (se consideră produsul scalar uzual şi norma indusă de acesta). vi) Să se afle complementul ortogonal al lui \( S_{2} \). 1. Construir um retăngulo sendo dados os comprimentos de um lado e de uma diagonal. 5. Which transformation is the same as reflecting a triangle over the \( x \)-axis, then the \( y \)-axis? ¿Qué transformación es lo mismo que reflejar un triángulo sobre el eje \( x \), luego el eje \( y \) ? (Page 47,55\( )(0.5 \mathrm{pt}) \) \( \begin{array}{ll}\text { A. Rotating } \triangle A B C 90^{\circ} & \text { B. Rotating } \triangle A B C 180^{\circ} \\ \text { C. Rotating } \triangle A B C 270^{\circ} & \text { D. Rotating } \triangle A B C 360^{\circ}\end{array} \) 4. Which of the following properties do all rigid motions NOT preserve? ¿Cuál de las siguientes propiedades NO conservan todos los movimientos rígidos? (Page 43,55\( )(0.5 \mathrm{pt}) \) \( \begin{array}{lll}\text { A. Orientation } & \text { B. Collinearity } & \text { C. Angle Measure }\end{array} \) Circle \( J \) is located in the first quadrant with center \( (a, b) \) and radius \( s \). Felipe transforms Circle \( J \) to prove that it is similar to any circle centered at the origin with radius \( t \). Which sequence of transformations did Felipe use? (A) Translate Circle \( J \) by \( (x+a, y+b) \) and dilate by a factor of \( \frac{t}{S} \). Translate Circle \( J \) by \( (x+a, y+b) \) and dilate by a factor of \( \frac{S}{t} \). (C) Translate Circle \( J \) by \( (x-a, y-b) \) and dilate by a factor of \( \frac{t}{s} \). (D) Translate Circle \( J \) by \( (x-a, y-b) \) and dilate by a factor of \( \frac{S}{t} \). Question In \( \Delta \mathrm{VWX}, \mathrm{WX}=15, \mathrm{XV}=5 \), and \( \mathrm{VW}= \) 11. Which list has the angles of \( \Delta \mathrm{VWX} \) in order from smallest to largest? Answer \( \mathrm{m} \angle V, \mathrm{~m} \angle X, \mathrm{~m} \angle W \) \( \mathrm{~m} \angle X, \mathrm{~m} \angle W, \mathrm{~m} \angle V \) \( \mathrm{~m} \angle W, \mathrm{~m} \angle X, \mathrm{~m} \angle V \) \( \mathrm{~m} \angle V, \mathrm{~m} \angle W, \mathrm{~m} \angle X \) \( \mathrm{~m} \angle W, \mathrm{~m} \angle V, \mathrm{~m} \angle X \) \( \mathrm{~m} \angle X, \mathrm{~m} \angle V, \mathrm{~m} \angle W \) A distância \( x \) entre o ponto \( A \) e B é de aproximadamente A) 45 metros B) 50 metros C) 55 metros D) 58 metros
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