Question

Line segment AB is on the coordinate plane and has endpoints at A(-5,3) and B(1,8). What is the length of the line segment to the nearest hundredth?

A) 30.5 B) 11.0 C) 7.81 D) 3.32

Answer 1

AB = 7.81

Explanation:

Distance between 2 points = sqrt( (x2 - x1)^2 + (y2 - y1)^) )

x2 = - 5

x1 = 1

y2 = 3

y1 = 8

D = sqrt( -5 - 1)^2 + (3 - 8)^2 )

D = sqrt( (-6)^2 + (-5)^2 )

D = sqrt( (36 + 25)

D = sqrt( 61)

D = 7.81

Answer 2

C) 7.81

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 = √((x_2-x_1)^2+(y_2-y_1)^2)`

Explanation:

Step 1: Define

Identify

Point A(-5, 3)

Point B(1, 8)

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 = √((1--5)^2+(8-3)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((6)^2+(5)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(36+25)`
4. [√Radical] Add:
   `\displaystyle d = √(61)`
5. [√Radical] Evaluate:
   `\displaystyle d = 7.81025`
6. Round:
   `\displaystyle d \approx 7.81`