Is the point (1/2 , 1/2) on the unit circle?

Question

A. Yes
B. No
Explain how you know if (1/2 , 1/2) is on the unit circle by showing the steps that led to your answer

Answer 1

To determine if the point \( (1/2, 1/2) \) is on the unit circle, we need to use the equation of the unit circle, which is:

\[ x^2 + y^2 = 1 \]

For the point \( (1/2, 1/2) \), we can substitute \( x = 1/2 \) and \( y = 1/2 \) into the equation.

1. Calculate \( x^2 \): \[ \left( \frac{1}{2} \right)^2 = \frac{1}{4} \]

2. Calculate \( y^2 \): \[ \left( \frac{1}{2} \right)^2 = \frac{1}{4} \]

3. Add \( x^2 \) and \( y^2 \): \[ x^2 + y^2 = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} \]

4. Now check if this sum equals 1: \[ \frac{1}{2} \neq 1 \]

Since \( x^2 + y^2 = \frac{1}{2} \) does not equal 1, the point \( (1/2, 1/2) \) is not on the unit circle.

Thus, the answer is: B. No