Gọi `\vec{n}_(AB)=(a; b)`

`-> AB: a(x-4)+b(y-1)=0`

`-> ax+by-4a-b=0`

$\triangle$ $ABC$ vuông cân tại $A$

`->` $\widehat{B}=45^o$

`->` $\cos(\widehat{B})=\cos(AB; BC)=$ `(|3a-b|)/(\sqrt{a^2+b^2}.\sqrt{3^2+(-1)^2})=(\sqrt{2})/(2)`

`-> 2|3a-b|=2\sqrt{5}\sqrt{a^2+b^2}`

`-> 36a^2+24ab+4b^2=20a^2+20b^2`

`-> 16a^2-24ab-16b^2=0`

`-> a=2b` hoặc `a=(-b)/(2)`

_ Khi `a=2b -> a=2; b=1`

`-> AB: 2x+y-9=0`

`-> AC: x-2y+c=0` `(AB` $\bot$ `AC)` đi qua $A(4; 1)$

`-> 4-2.1+c=0`

`-> c=-2`

`-> AC: x-2y-2=0`

_ Khi `a=(-b)/(2) -> a=1; b=-2`

`-> AB: x-2y-2=0`

`-> AC: 2x+y-9=0` `(AB` $\bot$ `AC)`