Is the point (1/2, 1/2) on the unit circle?(1 point) Responses Yes Yes No No Question 2 Explain how you know if (1/2, 1/2) is on the unit circle by either: a) Explaining in words or b) Showing the mathematical steps that led to your answer

Question

GPT-4o mini · Answer

To determine if the point $(1/2, 1/2)$ is on the unit circle, we can use the definition of the unit circle. The unit circle is defined as the set of all points $(x, y)$ in a Cartesian coordinate system that are a distance of 1 from the origin $(0, 0)$. Mathematically, this is expressed by the equation: $$ x^2 + y^2 = 1 $$ Now we can check whether the point $(1/2, 1/2)$ satisfies this equation. 1. Plug in $x = 1/2$ and $y = 1/2$ into the equation: $$ \left(\frac{1}{2}\right)^2 + \left(\frac{1}{2}\right)^2 = 1 $$ 2. Calculate each term: $$ \frac{1}{4} + \frac{1}{4} = 1 $$ 3. Combine the terms: $$ \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $$ Since $\frac{1}{2} \neq 1$, the point $(1/2, 1/2)$ does not satisfy the equation of the unit circle. Therefore, the answer is **No**, the point $(1/2, 1/2)$ is not on the unit circle.