Question

Which of the following could be points on the unit circle?

A. (1/3,2/3)
B. (4/3,4/5)
C. (6/7, sqrt 13/7)
D. (5/13, 12/13)

Answer 1

The problem ask to choose among the following choices that could be points on the unit circle and the best answer among these choice is letter C. I hope you are satisfied with my answer and feel free to ask for more if you have clarification and further questions. Have a nice day 

Answer 2

The correct option is D.

Step-by-step 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:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Find the distance of given points from the origin.

Distance of (1/3,2/3) from the origin is

`D_A=\sqrt{((1)/(3)-0)^2+((2)/(3)-0)^2}=\sqrt{(5)/(9)}\\eq 1`

Distance of (4/3,4/5) from the origin is

`D_B=\sqrt{((4)/(3)-0)^2+((4)/(5)-0)^2}=\sqrt{(544)/(225)}\\eq 1`

Distance of (6/7, sqrt 13/7) from the origin is

`D_C=\sqrt{((6)/(7)-0)^2+(\sqrt{(13)/(7)}-0)^2}=\sqrt{(127)/(49)}\\eq 1`

Distance of (5/13, 12/13) from the origin is

`D_D=\sqrt{((5)/(13)-0)^2+((12)/(13)-0)^2}=√(1)=1`

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.