Answer:
The correct option is D.
Explanation:
Unit circle is a circle whose radius is 1 unit. The center of a unit circle is origin, i.e., (0,0).
Distance formula:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Find the distance of given points from the origin.
Distance of (1/3,2/3) from the origin is
[tex]D_A=\sqrt{(\frac{1}{3}-0)^2+(\frac{2}{3}-0)^2}=\sqrt{\frac{5}{9}}\neq 1[/tex]
Distance of (4/3,4/5) from the origin is
[tex]D_B=\sqrt{(\frac{4}{3}-0)^2+(\frac{4}{5}-0)^2}=\sqrt{\frac{544}{225}}\neq 1[/tex]
Distance of (6/7, sqrt 13/7) from the origin is
[tex]D_C=\sqrt{(\frac{6}{7}-0)^2+(\sqrt{\frac{13}{7}}-0)^2}=\sqrt{\frac{127}{49}}\neq 1[/tex]
Distance of (5/13, 12/13) from the origin is
[tex]D_D=\sqrt{(\frac{5}{13}-0)^2+(\frac{12}{13}-0)^2}=\sqrt{1}=1[/tex]
The distance between (5/13, 12/13) and origin is 1, it means the point (5/13, 12/13) lie on the unit circle. Therefore the correct option is D.
