Question

What is the approximate distance between points A and B?

A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair 1, 4 is labeled as A, and the ordered pair negative 2, negative 3 is labeled as B.

a. 6.32
b. 6.95
c. 7.62
d. 8.56

Answer 1

`\displaystyle d \approx 7.62`

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 II

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

Explanation:

Step 1: Define

Find points from graph.

Point A(1, 4)

Point B(-2, -3)

Step 2: Find distance d

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

1. Substitute in points [DF]:
   `\displaystyle d = √((-2-1)^2+(-3-4)^2)`
2. (Parenthesis) Subtract:
   `\displaystyle d = √((-3)^2+(-7)^2)`
3. [√Radical] Exponents:
   `\displaystyle d = √(9+49)`
4. [√Radical] Add:
   `\displaystyle d = √(58)`
5. [√Radical] Evaluate:
   `d = 7.61577`
6. Round:
   `\displaystyle d \approx 7.62`