Question

Cho A(3;1);vt AB(1;1).Tìm tọa độ điểm M Sao cho AM = 2 Và ( vtAB,vtAM )=135 độ

Answer 1

vecto AB=(1;1)

vecto AM=(x-3;y-1)

\(\left(\overrightarrow{AB},\overrightarrow{AM}\right)=135^0\)

\(\Leftrightarrow\dfrac{1\cdot\left(x-3\right)+1\left(y-1\right)}{\sqrt{1^2+1^2}\cdot\sqrt{\left(x-3\right)^2+\left(y-1\right)^2}}=-\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow\dfrac{x+y-4}{\sqrt{\left(x-3\right)^2+\left(y-1\right)^2}}=-1\)

=>\(x+y-4=-\sqrt{\left(x-3\right)^2+\left(y-1\right)^2}\)

=>\(x=-y+4-\sqrt{\left(x-3\right)^2+\left(y-1\right)^2}\)

AM=2 nên \(\sqrt{\left(x-3\right)^2+\left(y-1\right)^2}=2\)

=>x=-y+4+2=-y+2

=>M(-y+2;y)