`BC: x+7y-13=0`

`-> x=13-7y`

Gọi `M(13-7m; m)` là trung điểm $BC$

`-> ME=MF` (cùng `=(1)/(2)BC`)

`-> ME^2=MF^2`

`-> [2-(13-7m)]^2+(5-m)^2=[0-(13-7m)]^2+(4-m)^2`

`-> (7m-11)^2+(m-5)^2=(7m-13)^2+(m-4)^2`

`-> 49m^2-154m+121+m^2-10m+25=49m^2-182m+169+m^2-8m+16`

`-> m=(3)/(2)`

`-> M((5)/(2); (3)/(2))`

Gọi `B(13-7b; b)`

Mà `M((5)/(2); (3)/(2))` là trung điểm `BC`

`-> C(7b-8; 3-b)`

`->` `\vec{BE}=(7b-11; 5-b);` `\vec{CE}=(10-7b; b+2)`

Mà `\vec{BE}.\vec{CE}=0` (vì `BE` $\bot$ `AC`)

`-> (7b-11; 5-b).(10-7b; b+2)=0`

`-> (7b-11)(10-7b)+(5-b)(b+2)=0`

`-> 70b-49b^2-110+77b+5b+10-b^2-2b=0`

`-> 50b^2-150b+100=0`

`-> b^2-3b+2=0`

`-> (b-1)(b-2)=0`

`-> b=1` hoặc `b=2`

_ Khi `b=1 -> B(6; 1); C(-1; 2)`

`-> A((2)/(3); (11)/(3))`

_ Khi `b=2 -> B(-1; 2); C(6; 1)`

`-> A(1; 6)`