Which of the following point is nearest point to origin? A) (2, -3) 

Correct option is (D) (1, 3)

(A) Distance between point (2, -3) to origin (0, 0) is

\(d=\sqrt{(0-2)^2+(0-(-3))^2}\)

\(=\sqrt{4+9}=\sqrt{13}\)

(B) Distance between point (5, 0) to origin (0, 0) is

\(d=\sqrt{(0-5)^2+(0-0)^2}\)

\(=\sqrt{25}=5\)

(C) Distance between point (0, -5) to origin (0, 0) is

\(d=\sqrt{(0-0)^2+(0-(-5))^2}\)

\(=\sqrt{25}=5\)

(D) Distance between point (1, 3) to origin (0, 0) is

\(d=\sqrt{(0-1)^2+(0-3)^2}\)

\(=\sqrt{1+9}=\sqrt{10}\)

\(\because\sqrt{10}<\sqrt{13}<5\)

\(\therefore\) Among given points (1, 3) is nearest point to origin.

Correct option is D) (1, 3)