Test whether the point is on the unit circle by plugging it into the equation, $x^2+y^2=1$.
$\left(\frac{-\sqrt2}{2},\frac{-\sqrt2}{2}\right)$

• A. On Unit Circle
• B. NOT on Unit Circle
• C. More information is required

Answer: (A)

Verified step by step guidance

1. Step 1: Recall the equation of the unit circle, which is given by $x^2\; +\; y^2\; =\; 1$. Any point that satisfies this equation lies on the unit circle.
2. Step 2: Substitute the given point $\backslash left(\backslash frac\{-\backslash sqrt\{2\}\}\{2\},\; \backslash frac\{-\backslash sqrt\{2\}\}\{2\}\backslash right)$ into the equation. Replace $x$ with $\backslash frac\{-\backslash sqrt\{2\}\}\{2\}$ and $y$ with $\backslash frac\{-\backslash sqrt\{2\}\}\{2\}$.
3. Step 3: Compute the squares of the $x$ and $y$ values. For $x^2$, calculate $\backslash left(\backslash frac\{-\backslash sqrt\{2\}\}\{2\}\backslash right)^2$. Similarly, for $y^2$, calculate $\backslash left(\backslash frac\{-\backslash sqrt\{2\}\}\{2\}\backslash right)^2$.
4. Step 4: Add the results of $x^2$ and $y^2$. Simplify the expression to check if the sum equals 1.
5. Step 5: Based on the result of the calculation, determine whether the point lies on the unit circle. If $x^2\; +\; y^2\; =\; 1$, the point is on the unit circle. Otherwise, it is not.