Question

Plot and Find Area of Polygon (Rectilinear Lengths)
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A, left parenthesis, minus, 3, comma, 2, right parenthesisA(−3,2), B, left parenthesis, 5, comma, 2, right parenthesisB(5,2), C, left parenthesis, 5, comma, minus, 7, right parenthesisC(5,−7), D, left parenthesis, minus, 3, comma, minus, 7, right parenthesisD(−3,−7), E, left parenthesis, minus, 3, comma, minus, 4, right parenthesisE(−3,−4), F, of, 1, comma, minus, 4F(1,−4), G, of, minus, 3, comma, minus, 1G(−3,−1)
Area =
unitssquared
2

Answer 1

To solve this problem, we will first plot the given points and then connect them in the specified order to form a polygon. After that, we will calculate the area of the resulting figure.

### Given Points:
- A (-3, 2)
- B (5, 2)
- C (5, -7)
- D (-3, -7)
- E (-3, -4)
- F (1, -4)
- G (-3, -1)

### Step 1: Plot the Points
1. **A (-3, 2)**
2. **B (5, 2)**
3. **C (5, -7)**
4. **D (-3, -7)**
5. **E (-3, -4)**
6. **F (1, -4)**
7. **G (-3, -1)**

### Step 2: Connect the Points
Connect the points in the order A → B → C → D → E → F → G.

### Step 3: Draw the Polygon
The polygon will appear as follows when you connect the points:

- Start at A (-3, 2) and move to B (5, 2) → horizontal line
- Move from B to C (5, -7) → vertical line
- Move from C to D (-3, -7) → horizontal line
- Move from D to E (-3, -4) → vertical line
- Move from E to F (1, -4) → horizontal line
- Move from F to G (-3, -1) → vertical line
- Finally, connect G back to A (-3, 2).

### Step 4: Calculate the Area
To find the area of the polygon, we can use the Shoelace Theorem (or any suitable method), but due to the rectilinear structure of the polygon, we will calculate the area based on the coordinates.

1. Divide the polygon into simpler segments (rectangles and triangles).
2. Calculate the area of each segment.

#### Area Calculation
1. **Rectangle A-B-C-D**
- Width = B.x - A.x = 5 - (-3) = 8
- Height = A.y - D.y = 2 - (-7) = 9
- Area = Width × Height = 8 × 9 = **72** square units.

2. **Rectangle D-E-F-G**
- For D (-3, -7) to E (-3, -4),
- The width (horizontal leg) = F.x - E.x = 1 - (-3) = 4 units
- The height (vertical leg) = E.y - D.y = -4 - (-7) = 3 units.
- Area = Width × Height = 4 × 3 = **12** square units.

#### Total Area
The total area of the polygon is:
\[ \text{Total Area} = \text{Area of Rect A-B-C-D} - \text{Area of Rect D-E-F-G} \]
\[ \text{Total Area} = 72 + 12 = 84 \text{ square units]}

**Final Result:**
The area of the polygon constructed by connecting the points in the stated order is \( 84 \) square units.