To find the final image point, we will perform the transformations step by step:

Step 1: Translate Point $P(-5, 7)$

• Four units right: Add 4 to the x-coordinate:
  $-5 + 4 = -1$
• Nine units down: Subtract 9 from the y-coordinate:
  $7 - 9 = -2$

Thus, after translation, the point becomes $(-1, -2)$.

Step 2: Reflect Over the X-Axis

• In reflection over the x-axis, the x-coordinate remains the same, but the y-coordinate is negated.
  $x = -1$ (no change)
  $y = -(-2) = 2$

Thus, the final image point is $(-1, 2)$.

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Would you like me to elaborate further on any part of the transformations? Here are five related questions to deepen your understanding:

1. What happens when a point is reflected over the y-axis instead of the x-axis?
2. Can you describe the effect of translating a point diagonally?
3. How do you find the midpoint between the original point and the final image?
4. What is the formula for a general reflection over the origin?
5. What changes if the translation happens before the reflection?

Tip: Always apply transformations step-by-step and verify the order of operations in composite transformations!