a. Draw a four-quadrant graph and label each axis. Plot the following ordered pairs: , ( ). Connect the points in the order given as you plot them,
comnect the tourth point to the first one.
b. Describe the shape on your graph. What is its area?

Ask by Mcfarlane Chandler. in the United States

Jan 17,2025

Question

a. Draw a four-quadrant graph and label each axis. Plot the following ordered pairs: , ( ). Connect the points in the order given as you plot them,
comnect the tourth point to the first one.
b. Describe the shape on your graph. What is its area?

Ask by Mcfarlane Chandler. in the United States

Jan 17,2025

UpStudy AI · Accepted Answer

Sure! Let's walk through each part of your problem step by step.

---

### **a. Drawing the Four-Quadrant Graph and Plotting the Points**

1. **Draw the Coordinate Axes:**
   - Draw two perpendicular lines intersecting at the origin (0,0).
   - Label the horizontal axis as the **x-axis** and the vertical axis as the **y-axis**.
   - Ensure that both axes extend into all four quadrants:
     - **Quadrant I:** (+x, +y)
     - **Quadrant II:** (-x, +y)
     - **Quadrant III:** (-x, -y)
     - **Quadrant IV:** (+x, -y)

2. **Plot the Given Ordered Pairs:**
   
   Let's plot each point one by one:

- **Point A: (-3, 2)**
     - Move 3 units to the left of the origin along the x-axis.
     - Move 2 units up along the y-axis.
     - Mark the point and label it **A(-3, 2)**.

- **Point B: (-8, 2)**
     - Move 8 units to the left of the origin along the x-axis.
     - Move 2 units up along the y-axis.
     - Mark the point and label it **B(-8, 2)**.

- **Point C: (-10, 8)**
     - Move 10 units to the left of the origin along the x-axis.
     - Move 8 units up along the y-axis.
     - Mark the point and label it **C(-10, 8)**.

- **Point D: (-5, 8)**
     - Move 5 units to the left of the origin along the x-axis.
     - Move 8 units up along the y-axis.
     - Mark the point and label it **D(-5, 8)**.

3. **Connect the Points in Order:**
   
   Connect the points in the following sequence:
   
   - **A → B → C → D → A**

This means:
   
   - Draw a line from **A(-3, 2)** to **B(-8, 2)**.
   - Then, draw a line from **B(-8, 2)** to **C(-10, 8)**.
   - Next, draw a line from **C(-10, 8)** to **D(-5, 8)**.
   - Finally, draw a line from **D(-5, 8)** back to **A(-3, 2)**.

---

### **b. Describing the Shape and Calculating Its Area**

#### **1. Describing the Shape**

By connecting the points **A → B → C → D → A**, the shape formed is a **trapezoid**. Here's why:

- **Trapezoid Definition:** A quadrilateral with at least one pair of parallel sides.
  
- **Identifying Parallel Sides:**
  
  - **AB** and **CD**:
    - **AB:** From (-3, 2) to (-8, 2) → Both points have the same y-coordinate (2), so **AB** is horizontal.
    - **CD:** From (-10, 8) to (-5, 8) → Both points have the same y-coordinate (8), so **CD** is horizontal.
    - Since both **AB** and **CD** are horizontal and lie on different y-levels, they are **parallel**.

Therefore, the shape is a **trapezoid** with **AB** and **CD** as the parallel sides.

#### **2. Calculating the Area**

The area $$ A $$ of a trapezoid can be calculated using the formula:

$$
A = \frac{1}{2} \times (b_1 + b_2) \times h
$$

Where:
- $$ b_1 $$ and $$ b_2 $$ are the lengths of the two parallel sides.
- $$ h $$ is the height (the perpendicular distance between the parallel sides).

**Let's determine each component:**

1. **Lengths of the Parallel Sides ($$ b_1 $$ and $$ b_2 $$):**

- **Length of AB ($$ b_1 $$):**
     - Both points have y = 2.
     - Distance along the x-axis: $$ |-3 - (-8)| = |5| = 5 $$ units.

- **Length of CD ($$ b_2 $$):**
     - Both points have y = 8.
     - Distance along the x-axis: $$ |-10 - (-5)| = |-5| = 5 $$ units.

**Note:** Both **AB** and **CD** are 5 units long.

2. **Height ($$ h $$):**

- The height is the vertical distance between the two parallel sides.
   - Subtract the y-coordinates of AB and CD:
     - $$ h = 8 - 2 = 6 $$ units.

3. **Plugging Values into the Area Formula:**

$$
A = \frac{1}{2} \times (5 + 5) \times 6 = \frac{1}{2} \times 10 \times 6 = 5 \times 6 = 30 \text{ square units}
$$

**Therefore, the area of the trapezoid is **30 square units**.**

---

### **Visual Representation**

While I can't draw the graph here, here's a textual representation to help you visualize the trapezoid:

```
y-axis
|
|                D(-5,8)-----------C(-10,8)
|                |                   |
|                |                   |
|                |                   |
|                A(-3,2)-----------B(-8,2)
|
+-------------------------------------------- x-axis
```

- **AB** and **CD** are the top and bottom parallel sides.
- **AD** and **BC** are the non-parallel sides connecting the parallel sides.

---

If you plot these points on graph paper or using graphing software, you'll see the trapezoidal shape as described. The calculated area confirms the space enclosed by this shape.
The shape is a trapezoid with an area of 30 square units.

a. Draw a four-quadrant graph and label each axis. Plot the following ordered pairs: , ( ). Connect the points in the order given as you plot them,
comnect the tourth point to the first one.
b. Describe the shape on your graph. What is its area?

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Geometry Questions

a. Draw a four-quadrant graph and label each axis. Plot the following ordered pairs: , ( ). Connect the points in the order given as you plot them, comnect the tourth point to the first one. b. Describe the shape on your graph. What is its area?

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Geometry Questions

a. Draw a four-quadrant graph and label each axis. Plot the following ordered pairs: , ( ). Connect the points in the order given as you plot them,
comnect the tourth point to the first one.
b. Describe the shape on your graph. What is its area?