Question

Does the point ( 1/9 , 2/3) lie on the unit circle? REASONING Does the point (1/9, 2.3 ) lie on the unit circle? Yes No Explain how you know.

Answer 1

No, the point (1/9, 2/3) does not lie on the unit circle because its distance from the origin is not equal to 1.

Step-by-step explanation:

To determine if a point lies on the unit circle, we need to check if its distance from the origin is 1. The distance between the point (1/9, 2/3) and the origin (0,0) can be found using the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the values (1/9, 2/3) and (0,0) in the formula:

d = sqrt((1/9 - 0)^2 + (2/3 - 0)^2)
= sqrt((1/9)^2 + (2/3)^2)

= sqrt(1/81 + 4/9)
= sqrt(13/81)

Since sqrt(13/81) is not equal to 1, the point (1/9, 2/3) does not lie on the unit circle.