The point P (5, 3) was reflected in the origin to get the image P'.
Find the area of the figure PMP'N.

Answer

To solve the problem, we need to find the area of the figure PMP'N, where P is the point (5, 3) and P' is its reflection in the origin. Let's go through the steps systematically.

### Step 1: Find the coordinates of P'
The point P (5, 3) is reflected in the origin to get the image P'. The coordinates of the reflected point P' can be found by negating both the x and y coordinates of P.

**Calculation:**
- P = (5, 3)
- P' = (-5, -3)

### Step 2: Identify points M and N
We need to find points M and N, which are the projections of P and P' on the x-axis. The x-axis has a y-coordinate of 0.

**Coordinates:**
- M is the projection of P (5, 3) on the x-axis, so M = (5, 0).
- N is the projection of P' (-5, -3) on the x-axis, so N = (-5, 0).

### Step 3: Determine the area of the figure PMP'N
The figure PMP'N forms a parallelogram. The area of a parallelogram can be calculated using the formula:
\[ \text{Area} = \text{base} \times \text{height} \]

In this case:
- The base is the distance between points M and N.
- The height is the vertical distance from point P to the x-axis.

**Base Calculation:**
- Distance between M and N = |x-coordinate of M - x-coordinate of N| = |5 - (-5)| = |5 + 5| = 10 units.

**Height Calculation:**
- The height is the y-coordinate of point P, which is 3 units.

### Step 4: Calculate the area
Now we can calculate the area using the base and height.

**Area Calculation:**
\[ \text{Area} = \text{base} \times \text{height} = 10 \times 3 = 30 \text{ square units} \]

### Final Answer
The area of the figure PMP'N is **30 square units**.

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