https://file.aiquickdraw.com/mathbot/file/1727201747923can5azvj.jpg

The problem asks to determine the Cartesian notation vector that is *opposite* to the given vector on the grid.

From the diagram, the vector starts at the origin \((0, 0)\) and ends at the point \((5, 3)\), so the vector is \(\mathbf{v} = (5, 3)\).

To find the opposite vector, we reverse the direction, which means multiplying both components by \(-1\). 

Thus, the opposite vector is:
\[
-\mathbf{v} = (-5, -3)
\]

The correct answer is \(\boxed{[-5, -3]}\).

Would you like further details or clarifications? Here are five follow-up questions to expand your understanding:

1. How do you calculate the magnitude of a vector in 2D?
2. What is the significance of reversing a vector's direction in physics?
3. Can you explain how vectors are added or subtracted graphically?
4. How would you express the vector in polar coordinates?
5. What is the role of unit vectors in Cartesian notation?

**Tip**: Always double-check the signs of the components when finding the opposite of a vector.

Determine the Cartesian notation vector opposite to the given vector on the grid.

Learn how to determine the opposite of a vector from a graph. Understand the concept of vector reversal using Cartesian notation with a detailed solution. Ideal for students in Grades 8-10.

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