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

Answer:

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

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

Answer 2

Answer:

AB = 7.81

Step-by-step 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