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)

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:

Find the distance of given points from the origin.

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

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

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

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

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.

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i beleive a. is the only possible answer