Answer:
Explanation:
To determine which of the given points could not be on the unit circle, we need to recall that the unit circle has a radius of 1 and is centered at the origin (0, 0). Points on the unit circle satisfy the equation x^2 + y^2 = 1.
Let's analyze each option:
a. (0.8, -0.6)
If we square the x-coordinate (0.8) and the y-coordinate (-0.6) and sum them up, we get:
(0.8)^2 + (-0.6)^2 = 0.64 + 0.36 = 1
This point satisfies the equation x^2 + y^2 = 1, so it could be on the unit circle.
b. (-2/3, √5/3)
Squaring the x-coordinate (-2/3) and the y-coordinate (√5/3) and summing them up:
(-2/3)^2 + (√5/3)^2 = 4/9 + 5/9 = 9/9 = 1
This point also satisfies the equation x^2 + y^2 = 1, so it could be on the unit circle.
c. (√3/2, 1/3)
Squaring the x-coordinate (√3/2) and the y-coordinate (1/3) and summing them up:
(√3/2)^2 + (1/3)^2 = 3/4 + 1/9 = 9/12 + 4/12 = 13/12
The sum is not equal to 1, so this point does not satisfy the equation x^2 + y^2 = 1. Thus, it could not be on the unit circle.
d. (1, 1)
Squaring the x-coordinate (1) and the y-coordinate (1) and summing them up:
(1)^2 + (1)^2 = 1 + 1 = 2
The sum is not equal to 1, so this point does not satisfy the equation x^2 + y^2 = 1. Hence, it could not be on the unit circle.
In conclusion, the point c. (√3/2, 1/3) could not be on the unit circle.