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To translate a polygon's vertices 4 units to the right and 5 units down, we add \([4, -5]\) to each vertex's coordinates.

Given vertices:
\[
(-5, 3), (-1, 3), (1, 0), (-3, 0)
\]

Applying the transformation:
1. \((-5 + 4, 3 - 5) = (-1, -2)\)
2. \((-1 + 4, 3 - 5) = (3, -2)\)
3. \((1 + 4, 0 - 5) = (5, -5)\)
4. \((-3 + 4, 0 - 5) = (1, -5)\)

Now, let's check the options to see which matches this transformation:

1. The matrix in each option should show adding \(4\) to the x-coordinates and \(-5\) to the y-coordinates:
   \[
   \begin{bmatrix}
   4 & 4 & 4 & 4 \\
   -5 & -5 & -5 & -5 \\
   \end{bmatrix}
   \]

After checking the provided options, **the first option** is correct.

### Would you like more details or have any questions?

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### Related Questions
1. How do you perform a geometric translation on a coordinate plane?
2. What are the rules for translating a point in the coordinate plane?
3. How would you translate a polygon in other directions, such as up or left?
4. How can you find the coordinates of a shape after a sequence of transformations?
5. How does geometric translation differ from other transformations like rotation or reflection?

### Tip
In translations, always add or subtract values directly to the x and y coordinates. A positive x value moves right, and a positive y value moves up.

A polygon has vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0). Which represents a geometric translation of the given polygon 4 units to the right and 5 units down?

Solve a problem on translating a polygon with vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0) by moving it 4 units to the right and 5 units down. This problem involves understanding coordinate geometry and matrix operations, ideal for students in Grades 8-10.

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