Question

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

A. ( 5/13, 12/13)
B. (6/7, pi13/ 7)
C. (1/3, 2/3)
D. (4/3, 4/5)​

Answer 1

Points A and C are on the unit circle

Explanation:

The unit circle is a circle of radius 1, that is, all the points that are inside the circle have the sum of the squares of its coordinates that are at most 1. Here, we have to test this for each option.

In options B and D, the coordinates 13/7 and 4/3, respectively, means that this sum will be larger than 1, and this points will not be on the unit circle. Now we text for options A and C.

A. ( 5/13, 12/13)

`\sqrt{((5)/(13))^2+((12)/(13))^2} = \sqrt{(25)/(169)}+\sqrt{(144)/(169)} = \sqrt{(169)/(169)} = √(1) = 1`

Since the sum of the squares is 1, the point is on the unit circle.

C. (1/3, 2/3)

`\sqrt{((1)/(3))^2+((2)/(3))^2} = \sqrt{(1)/(9)}+\sqrt{(4)/(9)} = \sqrt{(5)/(9)}`

Since the sum of the squares is less than 1, the point is on the unit circle.