-3x - 4y - 44 = -
-4y = 3x + 44
y = (-3/4)x - 11
y₂ = a₂x + b
a₂ = -1/a
a₂ = -1/(-3/4)
a₂ = 4/3
y = (4/3)x + b ; P(2;0)
0 = (4/3)*2 + b
0 = 8/3 + b
b = -8/3
y = (4/3)x - 8/3
[tex]\left \{ {{y = \frac{4}{3} x - \frac{8}{3} } \atop {y = -\frac{3}{4} x - 11}} \right. \\\left \{ {{y = \frac{4}{3} x - \frac{8}{3} } \atop {\frac{4}{3} x - \frac{8}{3} = -\frac{3}{4} x - 11}} \right. \\\left \{ {{y = \frac{4}{3} x - \frac{8}{3} } \atop { \frac{4}{3} x +\frac{3}{4} x = - 11+ \frac{8}{3}}} \right.\\\left \{ {{y = \frac{4}{3}x - \frac{8}{3}} \atop {\frac{16}{12}x +\frac{9}{12}x= - \frac{33}{3} +\frac{8}{3} }} \right.[/tex]
[tex]\left \{ {{y = \frac{4}{3}x - \frac{8}{3}} \atop {\frac{25}{12}x = - \frac{25}{3} }} \right.\\\left \{ {{y = \frac{4}{3}x - \frac{8}{3}} \atop {x = - \frac{25}{3}*\frac{12}{25} }} \right.\\\left \{ {{y = \frac{4}{3}x - \frac{8}{3}} \atop {x = - 4 }} \right.\\\left \{ {{y = \frac{4}{3}*(-4) - \frac{8}{3}} \atop {x = - 4 }} \right.\\\left \{ {{y = -\frac{16}{3} - \frac{8}{3}} \atop {x = - 4 }} \right.\\\left \{ {{y = -\frac{24}{3}} \atop {x = - 4 }} \right.\\[/tex]
[tex]\left \{ {{y = -8} \atop {x = - 4 }} \right.[/tex]
punkt należący do prostej y: P₂ = (-4;-8)
[tex]|PP_{2}| = \sqrt{(-4-2)^{2}+(-8-0)^{2}} = \sqrt{(-6)^{2} + (-8)^{2}}= \sqrt{36 + 64} = \sqrt{100} = 10[/tex]
Odp: Odległosć punktu P(2,0) od prostej -3x-4y-44=0, jest równa 10.
