The polar coordinates of a point are given. Find the rectangular coordinates of this point. \[ \left(-2, \frac{7 \pi}{4}\right) \] What are the rectangular coordinates of this point? (Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Step 1 ：The polar coordinates are given as \((-2, \frac{7 \pi}{4})\), where the first value is the distance from the origin (r) and the second value is the angle measured from the positive x-axis (θ).

Step 2 ：We can convert these polar coordinates to rectangular coordinates using the formulas: \(x = r\cos(θ)\) and \(y = r\sin(θ)\).

Step 3 ：Substituting the given values into these formulas, we get: \(x = -2\cos(\frac{7 \pi}{4})\) and \(y = -2\sin(\frac{7 \pi}{4})\).

Step 4 ：Solving these equations, we find that \(x = -\sqrt{2}\) and \(y = \sqrt{2}\).

Step 5 ：Thus, the rectangular coordinates of the point are \(\boxed{(-\sqrt{2}, \sqrt{2})}\).