Question

HELP PLEASE!!! 30 POINTS!!!!!

Answer 1

`\text{The fomula of a midpoint:}\\\\\left((x_1+x_2)/(2);\ (y_1+y_2)/(2)\right)`

`\text{N(2a, 0), M(0, 2b). Substitute:}\\\\x=(2a+0)/(2)=(2a)/(2)=a\\\\y=(0+2b)/(2)=(2b)/(2)=b\\\\\boxed{P(a,\ b)}`

`\text{The formula of a distance between two points:}\\\\d=√((x_2-x_1)^2+(y_2-y_1)^2)`

`\text{Calculate the distance OP}\ A(0,\ 0);\ P(a,\ b)\\\\|OP|=√(a-0)^2+(b-0)^2)=√(a^2+b^2)`

`\text{Answer}:\ \boxed{d.\ √(a^2+b^2)}`