The points U(0,−1), V(−8,−1), and W(0,−5) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.

Let's calculate the perimeter of the triangle formed by the points \( U(0, -1) \), \( V(-8, -1) \), and \( W(0, -5) \).

### Step 1: Plot the Points
- **U** = (0, -1)
- **V** = (-8, -1)
- **W** = (0, -5)

### Step 2: Calculate the Length of the Sides
We will use the distance formula to find the length of each side of the triangle.

1. **Length of \( UV \)**:
   \[
   UV = \sqrt{(0 - (-8))^2 + (-1 - (-1))^2} = \sqrt{8^2 + 0^2} = \sqrt{64} = 8
   \]

2. **Length of \( VW \)**:
   \[
   VW = \sqrt{(0 - (-8))^2 + (-5 - (-1))^2} = \sqrt{8^2 + (-4)^2} = \sqrt{64 + 16} = \sqrt{80} \approx 8.9
   \]

3. **Length of \( UW \)**:
   \[
   UW = \sqrt{(0 - 0)^2 + (-5 - (-1))^2} = \sqrt{0^2 + (-4)^2} = \sqrt{16} = 4
   \]

### Step 3: Calculate the Perimeter
The perimeter \( P \) of the triangle is the sum of the lengths of its sides:
\[
P = UV + VW + UW = 8 + 8.9 + 4 = 20.9
\]

### Final Answer
The perimeter of the triangle is **20.9 units**.

Would you like further details or have any questions?

### Relative Questions:
1. How do you determine if three points are collinear?
2. Can you explain the significance of the distance formula?
3. What are the properties of the centroid of a triangle?
4. How would you find the area of this triangle?
5. What are the different types of triangles based on side lengths and angles?

### Tip:
When calculating distances between points on a coordinate plane, ensure to carefully handle negative signs in the coordinates to avoid errors.

Learn how to calculate the perimeter of a triangle using the distance formula. Solve for the triangle formed by points U(0,-1), V(-8,-1), and W(0,-5) on a coordinate plane. Detailed step-by-step solution provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation