7. Di un rombo \( A B C D \) si conoscono il vertice \( A(0,-1) \), il punto medio \( M(2,0) \) della diagonale \( A C \) e si sa che il vertice \( B \) appartiene alla bisettrice del primo e del terzo quadrante. Determina i restanti vertici del rombo \( A B C D \) e calcola larea del rombo. 8. Nella figura i punti \( A, B, C \).

In a right triangle, the lengths of the legs are given as 12 units and 5 units. Use the Pythagorean theorem to find the length of the hypotenuse.

In the figure below, the chord \( E F \) subtends angle of \( 114^{\circ} \) at the centre \( O \). Calculate (a) the length of the chord \( E F \),

Find equation of straight line through \( (-1,4) \) and perpendicular to the line passing through \( (3,0) \) and \( (1,-2) \).

Soit \( A B C \) un triangle. Eet \( F \) deux points tel que: \( \overrightarrow{B E}=2 \overrightarrow{A C} \quad \) et \( \overrightarrow{C F}=\frac{1}{2} \overrightarrow{A B} \) 1) Construire les points \( E \) et \( F \). 2) Montrer que : \( \overrightarrow{A E}=\overrightarrow{A B}+2 \overrightarrow{A C} \quad \) et \( \overrightarrow{A F}=\frac{1}{2} \overrightarrow{A B}+\overrightarrow{A C} \)

6. ABCD is a quadrilateral, and AC and BD are its diagonals. Is \( \mathrm{AB}+\mathrm{BC}+\mathrm{CD}+\mathrm{DA}>\mathrm{AC}+\mathrm{BD} \) ? 7. ABCD is a quadrilateral and \( O \) is any point in its interior in the given figure Show that \( A B+B C+C D+D A<2(O A+O B+O C+O D) \).