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D নং প্রশ্নের উত্তর কি হবে?

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.

Explore how to analyze the quadrilateral formed by points O(0,0), P(3,-2), Q(-3,4), and A using vector analysis and coordinate geometry. This problem includes applying the distance and slope formulas to evaluate side lengths and angles, ideal for students in Grades 10-12.

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