Question

Find the distance and midpoint of a segment with the following endpoints: (5,-1) and (-9,-1)

Answer 1

`d = 14`

`(-2,-1)`

General Formulas and Concepts:

• Order of Operations: BPEMDAS
• Distance Formula:
  `d = √((x_2-x_1)^2+(y_2-y_1)^2)`
• Midpoint Formula:
  `((x_1+x_2)/(2),(y_1+y_2)/(2))`

Explanation:

Step 1: Define

(5, -1)

(-9, -1)

Step 2: Find distance d

1. Substitute:
   `d = √((-9-5)^2+(-1-(-1))^2)`
2. Simplify:
   `d = √((-9-5)^2+(-1+1)^2)`
3. Subtract/Add:
   `d = √((-14)^2+(0)^2)`
4. Evaluate:
   `d = √(196)`
5. Evaluate:
   `d = \14`

Step 3: Find Midpoint

1. Substitute:
   `((5-9)/(2),(-1-1)/(2))`
2. Subtract:
   `((-4)/(2),(-2)/(2))`
3. Divide:
   `(-2,-1)`