[tex]A(x_{A},y_{A})[/tex]
[tex]A(2,3)[/tex]
[tex]d:x+my+m+1=0[/tex]
[tex]a = 1[/tex]
[tex]b = m[/tex]
[tex]c = m + 1[/tex]
[tex]D(A,d)=3 \sqrt{2} [/tex]
[tex]D(A,d)=\frac{a\times x_{A}+b\times y_{A}+c}{\sqrt{{a}^{2}+{b}^{2}}}[/tex]
[tex] \frac{1 \times 2 + m \times 3 + m + 1}{ \sqrt{ {1}^{2} + {m}^{2} } } = 3 \sqrt{2} [/tex]
[tex] \frac{2 + 3m + 1}{ \sqrt{1 + {m}^{2} } } = 3 \sqrt{2} [/tex]
[tex] \frac{3m + 3}{ \sqrt{1 + {m}^{2} } } = 3 \sqrt{2} [/tex]
[tex]3m + 3 = 3 \sqrt{2} \times \sqrt{1 + {m}^{2} } \: | {( \: \: )}^{2} [/tex]
[tex] {(3m + 3)}^{2} = {(3 \sqrt{2}) }^{2} \times {( \sqrt{1 + {m}^{2} } )}^{2} [/tex]
[tex]9 {m}^{2} + 18m + 9 = 18(1 + {m}^{2} )[/tex]
[tex]9 {m}^{2} + 18m + 9 = 18 + 18 {m}^{2} [/tex]
[tex]18 {m}^{2} - 9 {m}^{2} - 18m + 18 - 9 = 0[/tex]
[tex]9 {m}^{2} - 18m + 9 = 0 \: | \div 9[/tex]
[tex] {m}^{2} - 2m + 1 = 0[/tex]
[tex] {(m - 1)}^{2} = 0[/tex]
[tex]m - 1 = 0 = > m = 1[/tex]
