Question

If you connect points W and X, What would be the distance between the two points?

*Hint draw the legs

Answer 1

`\displaystyle d = 12√(2)`

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

• Reading a Cartesian graph
• Coordinates (x, y)

Trigonometry

• [Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Algebra II

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

Explanation:

*Note: The Distance Formula is derived from the Pythagorean Theorem

Step 1: Define

Point W(-6, 4)

Point X(6, -8)

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 = √((6--6)^2+(-8-4)^2)`
2. (Parenthesis) Simplify:
   `\displaystyle d = √((6+6)^2+(-8-4)^2)`
3. (Parenthesis) Add/Subtract:
   `\displaystyle d = √((12)^2+(-12)^2)`
4. [√Radical] Exponents:
   `\displaystyle d = √(144 + 144)`
5. [√Radical] Add:
   `\displaystyle d = √(288)`
6. [√Radical] Simplify:
   `\displaystyle d = 12√(2)`