Question

What is the distance between (-5,7) and (4,2)? Round your answer to the nearest tenth (1 decimal).

Answer 1

`\displaystyle d \approx 10.3`

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

Cartesian Planes

• Coordinates

Algebra II

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

Explanation:

Step 1: Define

Identify points

(-5, 7)

(4, 2)

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 = √((4 + 5)^2 + (2 - 7)^2)`
2. [√Radical] (Parenthesis) Simplify:
   `\displaystyle d = √(9^2 + (-5)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(81 + 25)`
4. [√Radical] Simplify:
   `\displaystyle d = √(106)`
5. [Distance] Approximate:
   `\displaystyle d \approx 10.3`