Question

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

Answer 1

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

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

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

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

$\text{Answer}:\ \boxed{d.\ \sqrt{a^2+b^2}}$