Question

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

Answer 1

Answer:

$d = 14$

$(-2,-1)$

General Formulas and Concepts:

• Order of Operations: BPEMDAS
• Distance Formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
• Midpoint Formula: $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

Step 1: Define

(5, -1)

(-9, -1)

Step 2: Find distance d

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

Step 3: Find Midpoint

1. Substitute:                    $(\frac{5-9}{2},\frac{-1-1}{2})$
2. Subtract:                       $(\frac{-4}{2},\frac{-2}{2})$
3. Divide:                          $(-2,-1)$