Question

Find the distance between the points (4,-8) and (7-10).

Answer 1

Answer:

$\displaystyle d = \sqrt{13}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Coordinates (x, y)

Algebra II

• Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point (4, -8)

Point (7, -10)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

1. Substitute in points [DF]:                     $\displaystyle d = \sqrt{(7-4)^2+(-10+8)^2}$
2. (Parenthesis) Subtract/Add:                $\displaystyle d = \sqrt{(3)^2+(-2)^2}$
3. [√Radical] Exponents:                         $\displaystyle d = \sqrt{9+4}$
4. [√Radical] Add:                                    $\displaystyle d = \sqrt{13}$

Answer 2

Answer:

The distance between the points (4,-8) and (7-10)

$= \sqrt{ {(7 - 4)}^{2} + {( - 10 - ( - 8))}^{2} } \\ = \sqrt{ {(7 - 4)}^{2} + {( - 10 + 8)}^{2} } \\ = \sqrt{ {3}^{2} + { (- 2)}^{2} } \\ = \sqrt{9 + 4} \\ = \sqrt{13} \: units$

√13 is the right answer.