What point is symmetric with respect to the​ y-axis to the point left parenthesis StartFraction StartRoot 2 EndRoot Over 2 EndFraction comma StartFraction StartRoot 2 EndRoot Over 2 EndFraction right parenthesis
​?

The point symmetric with respect to the \( y \)-axis to the point \( \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) \) is found by changing the sign of the \( x \)-coordinate while keeping the \( y \)-coordinate the same. 

Thus, the symmetric point is:

\[
\left( -\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)
\]

Would you like any further details or explanations on this topic?

Here are five related questions for further exploration:
1. What is the symmetric point with respect to the \( x \)-axis for \( \left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right) \)?
2. How do you find the symmetric point with respect to the origin?
3. What is the general rule for finding symmetry across a line?
4. Can you describe the symmetry across the line \( y = x \)?
5. How do you reflect a point across the line \( y = -x \)?

**Tip**: Symmetry with respect to the \( y \)-axis involves negating the \( x \)-coordinate, while symmetry with respect to the \( x \)-axis involves negating the \( y \)-coordinate.

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

Discover how to find the point symmetric with respect to the y-axis for the given point (√2/2, √2/2). This solution uses the concept of reflection symmetry and applies the formula for symmetry across the y-axis. Suitable for students in Grades 8-10.

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