Use a graph paper for this question . (Take two divisions = 1 unit on both the axes.)
Plot the points P (3,2) and Q(-3,-2) . From P and Q , draw perpendiculars PM and QN on the x - axis.
Assign the special name to geometrical figure PMQN and find its area.

Answer

To solve the problem step by step, we will follow the instructions provided in the question.

### Step 1: Prepare the Graph Paper
- Use graph paper and ensure that each division on the graph paper represents 0.5 units (as 2 divisions = 1 unit).

**Hint:** Make sure to label the x-axis and y-axis clearly, and mark the origin (0,0).

### Step 2: Plot the Points P and Q
- Plot the point P(3, 2):
- Move 3 units to the right on the x-axis and 2 units up on the y-axis. Mark this point as P.

- Plot the point Q(-3, -2):
- Move 3 units to the left on the x-axis and 2 units down on the y-axis. Mark this point as Q.

**Hint:** Double-check your coordinates by counting the divisions on the graph paper.

### Step 3: Draw Perpendiculars PM and QN on the X-axis
- From point P(3, 2), draw a vertical line straight down to the x-axis. This line will intersect the x-axis at point M(3, 0).
- From point Q(-3, -2), draw a vertical line straight up to the x-axis. This line will intersect the x-axis at point N(-3, 0).

**Hint:** Ensure that the lines are straight and perpendicular to the x-axis.

### Step 4: Identify the Geometric Figure PMQN
- The points P, M, Q, and N form a quadrilateral. Since both PM and QN are vertical lines and MN is horizontal, the shape PMQN is a parallelogram.

**Hint:** Remember that opposite sides of a parallelogram are equal and parallel.

### Step 5: Find the Area of the Parallelogram PMQN
- The area of a parallelogram can be calculated using the formula:
\[ \text{Area} = \text{Base} \times \text{Height} \]
- Here, the base MN is the distance between points M and N:
- Distance MN = |3 - (-3)| = 6 units.

- The height (the vertical distance from P to the x-axis) is the y-coordinate of point P:
- Height = 2 units.

- Now, calculate the area:
\[ \text{Area} = \text{Base} \times \text{Height} = 6 \times 2 = 12 \text{ square units} \]

**Hint:** Make sure to use the correct base and height for the area calculation.

### Final Answer
The area of the parallelogram PMQN is **12 square units**.

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