Answer:
Option (A).
Step-by-step explanation:
From the figure attached,
ΔMON is a right triangle and coordinates of the points M and N are M(0, 2b) and N(2a, 0).
Coordinates of midpoint P → [tex](\frac{2a+0}{2}, \frac{0+2b}{2})[/tex]
→ (a, b)
From the formula of the distance between two points,
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
MN = [tex]\sqrt{(2a-0)^2+(0-2b)^2}[/tex]
= [tex]\sqrt{4a^2+4b^2}[/tex]
= 2[tex]\sqrt{a^2+b^2}[/tex]
Similarly, OP = [tex]\sqrt{(0-a)^2+(0-b)^2}[/tex]
= [tex]\sqrt{a^2+b^2}[/tex]
Therefore, OP = [tex]\frac{1}{2}(MN)[/tex]
and MN = [tex]\sqrt{4a^2+4b^2}[/tex] = 2[tex]\sqrt{a^2+b^2}[/tex]
Option (a) is the answer.
