a. ABCD là hbh \(\Leftrightarrow\overrightarrow{AB}=\overrightarrow{DC}\Leftrightarrow\left(1--2;-4--3\right)=\left(-5-x;3-y\right)\Leftrightarrow D\left(-8;4\right)\)
b. \(AB=\sqrt{\left(-2-1\right)^2+\left(-3--4\right)^2}=\sqrt{10}\)
\(OA=\sqrt{2^2+3^2}=\sqrt{13}\)
\(OB=\sqrt{1+4^2}=\sqrt{17}\)
=> chu vi tam giác OAB
\(BC=\sqrt{\left(1--5\right)^2+\left(-4-3\right)^2}=\sqrt{85}\)
\(AC=\sqrt{\left(-2--5\right)^2+\left(-3-3\right)^2}=\sqrt{85}\)
=> chu vi tam giác ABC
c. M(0;y)
\(AM=BM\Leftrightarrow\sqrt{2^2+\left(y+3\right)^2}=\sqrt{1+\left(y+4\right)^2}\Leftrightarrow y=-2\)
d. N(x;0)
\(NA=NB\Leftrightarrow\sqrt{\left(x+2\right)^2+3^2}=\sqrt{\left(x-1\right)^2+4^2}\Leftrightarrow x=\frac{2}{3}\)
