12. [s punti] In un trapezio isoscele la diffe- renza delle due basi misura 72 cm e l'altezza è \( \frac{2}{3} \) di questa differenza. Sapendo che l'area del trapezio è \( 3648 \mathrm{~cm}^{2} \) calcola l'area di un rettangolo avente le dimensioni lunghe quanto le due basi del trapezio. \( \begin{array}{lll}\text { a. } 4480 \mathrm{~cm}^{2} & \text { b. } 1600 \mathrm{~cm}^{2} & \text { c. } 2240 \mathrm{~cm}^{2}\end{array} \)

BCD un carré et \( G= \) bary \( \{(A, 2) ;(B,-1) ;(C, 2) ;(D ; 1)\} \) oient \( I= \) bary \( \{(A, 2) ;(B,-1)\} \) et \( J= \) bary \( \{(C, 2) ;(D ; 1)\} \); Montrer que \( 2 \overrightarrow{G A}-\overrightarrow{G B}=\overrightarrow{G I} \) et \( 2 \overrightarrow{G C}+\overrightarrow{G D}=3 \overrightarrow{G j} \) En déduire que \( G=\operatorname{bary\{ }(I, 1) ;(1,3)\} \) Construire I et \( J \) puis \( G \) a) Vérifier que: \( \forall M \in(P): 2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}=4 \overrightarrow{M G} \) b) Déterminer l'ensemble des points M du plan \( (P) \) tel que : \[ \|2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}\|=4\|2 \overrightarrow{M A}-\overrightarrow{M B}\| \]

\begin{tabular}{l|l|}\hline \( \begin{array}{l}\text { Sample Response: Because vertical angles are } \\ \text { congruent, angles } 1 \text { and } 4 \text { are congruent. Because } \\ \text { corresponding angles are congruent, angles } 4 \text { and } 8 \text { are } \\ \begin{array}{l}\text { congruent. Because angle } 4 \text { is congruent to both } 1 \text { and } 8, \\ \text { angle } 1 \text { is congruent to angle } 8 .\end{array}\end{array} \) & \( \begin{array}{l}\text { What did you include in your response? Check all that } \\ \text { apply. } \\ \square \text { vertical angles theorem } \\ \square \text { corresponding angles theorem } \\ \square \text { transitive property }\end{array} \) \\ \( \square \) supplementary angles \\ \( \square \) linear pairs \end{tabular}

4.4 \( g \) is one of the axes of symmetry of \( f \) and it is a decreasing function. Determine the equation of \( g \). 4.5 \( (-3 ; 2) \) is a point on \( f \). Determine the coordinates of the image of this point after reflection in \( g \).

A ball bounces \( \frac{1}{2} \) of its previous height on each bounce. Find the total distance covered by the ball, until it comes to rest, if it is dropped from a height of 20 metres.

Find the equation of line perpendicular to \( 5 x-3 y+4=0 \) that passes through the point \( (-4,1) \).