Question

Va rog sa ma ajutati cu aceasta problema!

Answer 1

$\it Gf\cap Ox=A(x,\ 0)\Rightarrow\ f(x)=0\Rightarrow\ 3x-6=0\Rightarrow\ 3x=6\Rightarrow\ x=2\Rightarrow\ A(2,\ 0)\\ \\ Gf\cap Oy=B(0,\ y)\ \Rightarrow\ y=f(0)=3\cdot0-6=-6\ \Rightarrow\ B(0,\ -6)\\ \\ M-\ simetricul\ lui\ A\ fa\c{\it t}\breve a\ de\ Oy\ \Rightarrow\ M(-2,\ 0)$

$\it \mathcal{A}_{AMB}=\dfrac{AM\cdot BO}{2}=\dfrac{4\cdot6}{2}=12\\ \\ MB^2=(x_B-x_M)^2+(y_B-y_M)^2=(0-2)^2+(-6-0)^2=4+36=40\\ \\ MB=\sqrt{40}=\sqrty{4\cdot10}=2\sqrt{10}\\ \\ \mathcal{A}_{AMB}=\dfrac{MB\cdot d(A,\ MB)}{2}\ \Rightarrow\ 12=\dfrac{\not2\sqrt{10}\cdot d(A,\ MB)}{\not2}\ \Rightarrow\ \\ \\ \\ \Rightarrow\ d(A,\ MB)=\dfrac{12}{\sqrt{10}}=\dfrac{12\sqrt{10}}{10}=1,2\sqrt{10}\approx1,2\cdot3,16\approx3,8\ u.\ m.$