a)

$A\left(1,-2\right)$

$x+y-5=0$  

Odległość punktu A od prostej 

$d=\frac{\left|1\cdot 1+\left(-2\right)\cdot 1-5\right|}{\sqrt{1^2+1^2}}=\frac{\left|1-2-5\right|}{\sqrt{2}}=\frac{6}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}=\frac{6\sqrt{2}}{2}=3\sqrt{2}$  

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b)

$A\left(1,-2\right)$

$3x+4y-8=0$  

Odległość punktu A od prostej

$d=\frac{\left|1\cdot 3+\left(-2\right)\cdot 4-8\right|}{\sqrt{3^2+4^2}}=\frac{\left|3-8-8\right|}{\sqrt{9+16}}=\frac{13}{\sqrt{25}}=\frac{13}{5}$  

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c)

$A\left(1,-2\right)$

$x-3y=-3$

$x-3y+3=0$   

Odległość punktu A od prostej

$d=\frac{\left|1\cdot 1+\left(-2\right)\cdot \left(-3\right)+3\right|}{\sqrt{1^2+{\left(-3\right)}^2}}=\frac{\left|1+6+3\right|}{\sqrt{10}}=\frac{10}{\sqrt{10}}\cdot \frac{\sqrt{10}}{\sqrt{10}}=\frac{10\sqrt{10}}{10}=\sqrt{10}$