Explicație pas cu pas:
[tex]f(x) = \frac{4}{3}x + 4 \\ [/tex]
intersecția cu axa Ox:
[tex]y = 0 => f(x) = 0 \\ \frac{4}{3}x + 4 = 0 < = > \frac{4}{3}x = - 4 \\ = > x = - 3 = > A\left(-3 ;0\right)[/tex]
intersecția cu axa Oy:
[tex]x = 0 => f(0) = 4 \\ = > B\left( 0;4\right)[/tex]
[tex]AB = \sqrt{ {(0 - ( - 3))}^{2} + {(4 - 0)}^{2} } = \sqrt{9 + 16} \\ = \sqrt{25} = 5 \\ [/tex]
[tex]M \in Oy => M\left(0 ;y_{M}\right)[/tex]
[tex]B, M \in Oy = > BM = |4 - y_{M}|[/tex]
[AB] ≡ [BM]
[tex] = > |4 - y_{M}| = 5[/tex]
[tex]4 - y_{M} = 5 \\ y_{M} = - 1 = > M_{1}\left(0 ; - 1\right)[/tex]
[tex]4 - y_{M} = - 5 \\ y_{M} = 9 = > M_{2}\left(0 ; 9\right)[/tex]
