To find the image point of $(-6, 9)$ after a translation of 4 units to the left and 1 unit down, follow these steps:

Step 1: Translate 4 units to the left.

• Subtract 4 from the x-coordinate. $-6 - 4 = -10$

Step 2: Translate 1 unit down.

• Subtract 1 from the y-coordinate. $9 - 1 = 8$

Final Answer:

The image point after the translation is $(-10, 8)$.

Would you like more details or have any other questions? Here are 5 related questions:

1. How would you translate a point if you move it 3 units to the right and 2 units up?
2. What is the effect of translating a point to the right on the coordinate plane?
3. How do you determine the direction of translation on a coordinate plane?
4. What is the image of the point (3, 7) after a translation 5 units to the left and 4 units down?
5. How can translations be represented using vector notation?

Tip: Translations only affect the coordinates, not the size or orientation of the object being moved.