Question

In the coordinate plane, what is the length of the line segment that connects points (3, -1) and (-5, 4), rounded to the nearest hundredth?

11.03
10.12
9.43
9.82

Answer 1

Answer:

$\displaystyle d \approx 9.43$

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

• Reading a Cartesian Plane
• 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 (3, -1)

Point (-5, 4)

Step 2: Find distance d

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

1. Substitute in coordinates [Distance Formula]:                                               $\displaystyle d = \sqrt{(-5-3)^2+(4--1)^2}$
2. [Distance] [√Radical] (Parenthesis) Subtract:                                                 $\displaystyle d = \sqrt{(-8)^2+(5)^2}$
3. [Distance] [√Radical] Evaluate exponents:                                                     $\displaystyle d = \sqrt{64+25}$
4. [Distance] [√Radical] Add:                                                                               $\displaystyle d = \sqrt{89}$
5. [Distance] [√Radical] Evaluate:                                                                        $\displaystyle d = 9.43398$
6. [Distance] Round:                                                                                             $\displaystyle d \approx 9.43$