Reflection Math Example 2

Solution

1. 1
   Step 1: The rule for reflection over the line $y = x$ is $(x, y) \to (y, x)$ — swap the coordinates.
2. 2
   Step 2: Apply to $Q(-2, 5)$: $Q' = (5, -2)$.
3. 3
   Step 3: Verify: the midpoint of $Q$ and $Q'$ should lie on $y=x$. Midpoint $= \left(\tfrac{-2+5}{2}, \tfrac{5+(-2)}{2}\right) = (1.5, 1.5)$. On $y=x$? Yes. ✓