The question (D) asks about the quadrilateral formed by the points O, P, Q, and A.

In the image:

• The points given are $O$ (the origin), $P(3, -2)$, and $Q(-3, 4)$.
• The vector $\overrightarrow{OA}$ is used, and the diagram shows vectors that connect these points.

The goal is to determine the nature of the quadrilateral formed by the points $O, P, Q,$ and $A$.

Let's summarize the analysis:

1. Coordinates:

   • $O(0, 0)$
   • $P(3, -2)$
   • $Q(-3, 4)$
   • Point $A$ is used to define vectors, but its exact coordinates are not given explicitly.

2. Type of Quadrilateral:

   • By analyzing the directions of the vectors, it seems the quadrilateral has different side lengths and angles.
   • Given the diagram's appearance and assuming vectors do not have equal magnitudes or directions, the quadrilateral is likely an irregular quadrilateral.

Therefore, the answer to (D) is:

The quadrilateral formed by the points O, P, Q, and A is an irregular quadrilateral.

Would you like more detailed calculations or further explanations? Here are some related questions for expanding your understanding:

1. What are the slopes of the lines $\overline{OP}$ and $\overline{OQ}$?
2. How can you calculate the length of the sides of the quadrilateral using distance formula?
3. How can you verify if a quadrilateral is a parallelogram or not?
4. What conditions are required for a quadrilateral to be a rectangle?
5. How do we calculate the area of a quadrilateral formed by four coordinates?

Tip: To identify the type of a quadrilateral, analyzing both the slopes and distances of all sides is crucial.