To find the image of the point $(-9, -7)$ after a translation 3 units to the right and 4 units up, we perform the following steps:

1. Translation right 3 units: Add 3 to the x-coordinate. $-9 + 3 = -6$
2. Translation up 4 units: Add 4 to the y-coordinate. $-7 + 4 = -3$

Therefore, the image point after the translation is $(-6, -3)$.

Would you like further details or have any questions?

Here are 5 related questions:

1. What happens to a point when translated left or down?
2. How would you translate a point by negative units?
3. What is the effect of translating a point along only one axis?
4. How do you find the distance between two points after translation?
5. How would you perform a reflection instead of a translation?

Tip: When translating a point, always adjust the x and y coordinates based on the direction and distance specified.