Question

Calculate the distance between the points B=(-2,1) and C=(2, -3) in the coordinate plane. Round your answer to the nearest hundredth.

Answer 1

`\displaystyle d \approx 5.66`

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

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

B(-2, 1)

C(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 [Distance Formula]:
   `\displaystyle d = √((2 + 2)^2 + (-3 - 1)^2)`
2. [√Radical] (Parenthesis) Simplify:
   `\displaystyle d = √(4^2 + (-4)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(16 + 16)`
4. [√Radical] Simplify:
   `\displaystyle d = √(32)`
5. [√Radical] Approximate:
   `\displaystyle d \approx 5.66`