Question

Cho ptdt d1: x+y=0, d2: x-y+1=0 dt d qua A(1;1) cat 2 dt d1, d2 lan luot tai B,C sao cho 2AB=AC.Tìm tọa độ B và C

Answer 1

Do \(B\in d_1\Rightarrow B\left(b;-b\right)\)

\(\overrightarrow{AB}=\left(b-1;-b-1\right)\)

Mà \(2AB=AC\Rightarrow2\overrightarrow{AB}=\overrightarrow{AC}=\left(2b-2;-2b-2\right)\)

\(\Rightarrow C\left(2b-1;-2b-1\right)\)

Mà \(C\in d_2\Rightarrow\left(2b-1\right)-\left(-2b-1\right)+1=0\)

\(\Leftrightarrow4b+1=0\Rightarrow b=\frac{-1}{4}\Rightarrow\left\{{}\begin{matrix}B\left(-\frac{1}{4};\frac{1}{4}\right)\\C\left(-\frac{3}{2};-\frac{1}{2}\right)\end{matrix}\right.\)