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

`\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 = √((x_2-x_1)^2+(y_2-y_1)^2)`

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 = √((-5-3)^2+(4--1)^2)`
2. [Distance] [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((-8)^2+(5)^2)`
3. [Distance] [√Radical] Evaluate exponents:
   `\displaystyle d = √(64+25)`
4. [Distance] [√Radical] Add:
   `\displaystyle d = √(89)`
5. [Distance] [√Radical] Evaluate:
   `\displaystyle d = 9.43398`
6. [Distance] Round:
   `\displaystyle d \approx 9.43`