Question

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Answer 1

$M_{x}=\frac{x_{O}+x_{B}}{2}=\frac{0+6}{2}=3\\\\M_{y}=\frac{y_O+y_B}{2}=\frac{0+6}{2}=3\\\\\iff M(3,3)\\\\\sout{ - - - - - - - - - - - - - - - - - - } \\ AO=\sqrt{(x_A-x_O)²+(y_A-y_O)²}\\AO=\sqrt{(6-0)²+(0-0)²}\\AO=\sqrt{36}\\AO=6\\\\AM=\sqrt{(x_A-x_M)²+(y_A-y_M)²}\\AM=\sqrt{(6-3)²+(0-3)²}\\AM=\sqrt{9+9}\\AM=3\sqrt{2}\\\\ OM=\sqrt{(x_O-x_M)²+(y_O-y_M)²}\\ OM=\sqrt{(0-3)²+(0-3)²}\\ OM=\sqrt{9+9}\\ OM=3\sqrt{2}\\\\\iff AM=OM\implies ΔAOM~\text{isoscel}$