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Home Question Bank Math Geometry Archive 2025 January 14

Geometry Questions from Jan 14,2025

Browse the Geometry Q&A Archive for Jan 14,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Are the lines given by the equations \( -4 x+y=5 \) and \( -x+4 y=12 \) parallel, perpendicular, or neither? Why? The line that passes through \( (3,5) \) and is parallel to the line through \( (3,3) \) and \( (-3,-1) \) \begin{tabular}{|l|}\hline 8. \\ Conducendo da un punto \( P \), esterno a una cir- \\ conferenza di centro \( O \) e raggio lungo \( 20 \mathrm{~cm}, ~ i \) \\ due segmenti di tangenza \( P A \) e \( P B \), si ottiene il \\ quadrilatero \( P A O B \). Sapendo che l'area del qua- \\ drilatero è \( 960 \mathrm{~cm}^{2} \), calcola la distanza del pun- \\ to \( P \) dal centro della circonferenza. \\ \end{tabular} Exercice 4 Soient \( A B C D \) est un parallélogramme et les points \( F \), I et E définis par: \( \overrightarrow{A F}=\frac{2}{3} \overrightarrow{A B} \), I milieu do [BC], E symétrique de I par rapport à B . 1) Faire une figure. 2) Exprimer \( \overrightarrow{C E} \) en fonction de \( \overrightarrow{C B} \). (Justifier) 3) Exprimer \( \overrightarrow{D F} \) et \( \overrightarrow{D F} \) en fonction de \( \overrightarrow{C B} \) et de \( \overrightarrow{A B} \). 4) En déduire que les points \( \mathrm{E}, \mathrm{F} \) et D sont alignés. 10. Determine if each statement is true or false. a. A square has perpendicular diagonals. b. A rhombus has congruent diagonals. c. A parallelogram has diagonals that bisect each other. d. A rectangle has diagonals that bisect each other. A. parallelogram's diagonals bisect opposite angles. f. A rectangle has perpendicular diagonals. g. A rhombus has four congruent sides. h. A square has four right angles. i. A parallelogram has congruent opposite sides. he line perpendicular to \( 3 x+y=8 \) that asses through \( (0,-2) \) The line that passes through \( (-2,3) \) and is perpendicular to the line through \( (0,1) \) and \( (-3,-1) \). \begin{tabular}{|l|}8. \\ Conducendo da un punto \( P \), esterno a una cir- \\ conferenza di centro 0 e raggio lungo \( 20 \mathrm{~cm}, ~ i \) \\ due segmenti di tangenza \( P A \) e \( P B \), si ottiene il \\ quadrilatero \( P A O B \). Sapendo che l'area del qua- \\ drilatero è \( 960 \mathrm{~cm}^{2} \), calcola la distanza del pun- \\ to \( P \) dal centro della circonferenza. \\ \\ \\ \hline 52 cm\( ] \) \\ \hline\end{tabular} The line perpendicular to \( y=-x+2 \) that passes through \( (-1,-7) \) \begin{tabular}{l} In una circonferenza con il raggio lungo 30 cm , \\ considera due corde parallele e situate dalla \\ stessa parte rispetto al centro. Sapendo che le \\ distanze delle due corde dal centro misurano \\ rispettivamente \( 8,4 \mathrm{~cm} \) e 18 cm , calcola l'area \\ del trapezio avente per basi le due corde. \\ [506,88 \( \left.\mathrm{cm}^{2}\right] \) \\ \hline\end{tabular}
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