The problem asks which diagram shows the result of translating the given figure down by 4 units and left by 3 units. Let’s go through this step by step.

1. Initial Position of the Figure: The original shape's top vertex seems to be at $(5, 4)$.

2. Translation:

   • Down by 4 units: Subtract 4 from the y-coordinates of all points. So, the top vertex will move from $(5, 4)$ to $(5, 0)$.
   • Left by 3 units: Subtract 3 from the x-coordinates. The top vertex will move from $(5, 0)$ to $(2, 0)$.

   Applying the same translation to the other points will similarly move the entire figure.

3. Final Position: The figure should now be positioned with its top vertex at $(2, 0)$, and the overall shape should maintain the same orientation and size, just shifted according to the translation.

By analyzing the options:

• Option A shows the correct translation, where the top vertex has moved to $(2, 0)$ and the entire figure is shifted as expected.

Thus, the correct answer is A.

Would you like further details or have any other questions?

Here are 5 related questions:

1. What is a geometric translation?
2. How would the transformation differ if we translated the figure up and right instead?
3. Can you explain the difference between translation and rotation?
4. How do translations affect the orientation of a figure?
5. What would happen if we applied multiple transformations in sequence?

Tip: When translating figures, make sure to adjust both the x- and y-coordinates correctly for each point.