Question

Which of the following points is on the unit cirlce?

Select one:
O a. (3/2, 2/3)
O b. (-√2/2,-√2/2)
O c. (1/2, 1/2)
O d. (√2/3, -√2/3)

Answer 1

Explanation:

The points that lie on the unit circle are the points (x, y) that satisfy the equation x^2 + y^2 = 1.

Let's check each option:

a. (3/2, 2/3)

(3/2)^2 + (2/3)^2 = 9/4 + 4/9 = 81/36 + 16/36 = 97/36 ≠ 1

b. (-√2/2, -√2/2)

(-√2/2)^2 + (-√2/2)^2 = 2/4 + 2/4 = 4/4 = 1

c. (1/2, 1/2)

(1/2)^2 + (1/2)^2 = 1/4 + 1/4 = 2/4 = 1/2 ≠ 1

d. (√2/3, -√2/3)

(√2/3)^2 + (-√2/3)^2 = 2/9 + 2/9 = 4/9 ≠ 1

Only option b. (-√2/2, -√2/2) has the coordinates that satisfy x^2 + y^2 = 1, making it the point that lies on the unit circle. Therefore, the correct answer is option:

O b. (-√2/2, -√2/2)