a)
[tex]\left \{ {{7=-a+b} \atop {0=-2a+b /*(-1)}} \right. \\\left \{ {{7=-a+b} \atop {0=2a-b}} \right. \\7=a\\7=-7+b /+7\\14=b\\y=7x+14\\\\7*a_2=-1\\a_2=-\frac17\\-5=-\frac17*3+b\\-5=-\frac37+b /+\frac37\\-\frac{35}7+\frac37=b\\-\frac{32}7=b\\-4\frac47=b\\y=-\frac17x-\frac{32}7\\[/tex]
[tex]\left \{ {{y=7x+14} \atop {y=-\frac17x-\frac{32}7}} \right. \\7x+14=-\frac17x-\frac{32}7 /*7\\49x+98=-x-32\\49x+x=-32-98\\50x=-130\\5x=-13\\x=-\frac{13}5=-2.6\\y=7*(-\frac{13}5)+14\\y=-\frac{91}5+\frac{70}5\\y=-\frac{21}5=-4.2\\P=(-2.6, -4.2)[/tex]
[tex]h=|CP|\\|CP|=\sqrt{(-2.6-3)^2+(-4.2+5)^2}=\sqrt{31.36+0.64}=\sqrt{32}=4\sqrt2\\h=4\sqrt2[/tex]
b)
[tex]P=ah=\frac{ef}2\\a=|AB|=|BC|=|CD|=|AD|\\|AB|=\sqrt{(-2+1)^2+(0-7)^2}=\sqrt{1+49}=\sqrt{50}=5\sqrt2\\P=5\sqrt2*4\sqrt2=20*2=40\\\\e=|AC|\\|AC|=\sqrt{(3+1)^2+(-5-7)^2}=\sqrt{16+144}=\sqrt{160}=4\sqrt{10}\\f=|BD|\\\\40=\frac{4\sqrt{10}*f}2 /*2\\80=4\sqrt{10}*f /:4\sqrt{10} \\f=\frac{80}{4\sqrt{10}}=\frac{20}{\sqrt{10}}=\frac{20\sqrt{10}}{10}=2\sqrt{10}\\|BD|=2\sqrt{10}[/tex]
