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.