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. Understand the unit circle equation: The unit circle is defined by the equation \(x^2 + y^2 = 1\). Any point \((x, y)\) that satisfies this equation lies on the unit circle.
2. Identify the coordinates of the point: The given point is \(\left(\frac{-\sqrt{2}}{2}, \frac{-\sqrt{2}}{2}\right)\).
3. Substitute the coordinates into the unit circle equation: Replace \(x\) with \(\frac{-\sqrt{2}}{2}\) and \(y\) with \(\frac{-\sqrt{2}}{2}\) in the equation \(x^2 + y^2 = 1\).
4. Calculate \(x^2\) and \(y^2\): Compute \(\left(\frac{-\sqrt{2}}{2}\right)^2\) for both \(x\) and \(y\).
5. Add the results: Sum the values of \(x^2\) and \(y^2\) to check if the result equals 1, confirming whether the point is on the unit circle.