To find the image point after a translation, you need to apply the translation to each coordinate of the original point.

The original point is $(3, -4)$.

1. Translation left 2 units: This means subtract 2 from the x-coordinate: $x' = 3 - 2 = 1$

2. Translation up 5 units: This means add 5 to the y-coordinate: $y' = -4 + 5 = 1$

So, the image point after the translation is $(1, 1)$.

Would you like more details on this process, or do you have any questions?

Here are 5 related questions you might find useful:

1. What is the image point of $(7, 2)$ after a translation 3 units to the right and 4 units down?
2. How do you translate a point when given a vector instead of direction and magnitude?
3. If a point $(x, y)$ is translated by $(a, b)$, what is the general formula for the new coordinates?
4. What is the effect of translating a point by $(-x, -y)$?
5. How would you determine the original point if only the translation and image point are known?

Tip: In coordinate geometry, translations preserve the shape and size of geometric figures.