Questions: What point is symmetric with respect to the y-axis to the point (sqrt(2)/2, -sqrt(2)/2)?

Solution Steps

A point \((x, y)\) is symmetric to another point with respect to the \( y \)-axis if its \( x \)-coordinate is the negative of the original point's \( x \)-coordinate, while the \( y \)-coordinate remains the same. Mathematically, the symmetric point is \((-x, y)\).

The given point is \(\left(\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)\). Here, \( x = \frac{\sqrt{2}}{2} \) and \( y = -\frac{\sqrt{2}}{2} \).

Using the symmetry rule, the symmetric point with respect to the \( y \)-axis is: \[ \left(-x, y\right) = \left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right). \]

Final Answer