Question

Which of the following is closest to the length

A: 7.2 units
B: 8 units
C: 10.8 units
D: 11.7 units

Answer 1

C: 10.8 units

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 coordinate plane
• Coordinates (x, y)

Algebra II

• Distance Formula:
  `\displaystyle d = √((x_2-x_1)^2+(y_2-y_1)^2)`

Explanation:

Step 1: Define

Identify points from graph

Point X(-8, 1)

Point Y(2, 5)

Step 2: Find distance d

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

1. Substitute in points [Distance Formula]:
   `\displaystyle d = √((2--8)^2+(5-1)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((10)^2+(4)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(100+16)`
4. [√Radical] Add:
   `\displaystyle d = √(116)`
5. [√Radical] Evaluate:
   `\displaystyle d = 10.7703`
6. Round:
   `\displaystyle d \approx 10.8`