Question

What is the distance between two points(0,0)(-3,5)

Answer 1

Explanation:

Think of it like a right triangle. Do you have a graph handy?

Ok, graph both of the points. Now connect the points. That's our hypotenuse and the side length we want to find.

Now, bring down a line from (-3,5) to the x axis. Do you see a right triangle?

All we have to do is find the hypotenuse of this right triangle we just drew. We already have the leg lengths which are 3 and 5. Using this, do the pythagorean theorem.

9+25=34

√34 is our hypotenuse & distance between the points

Answer 2

`\displaystyle d = √(34)`

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 = √((x_2-x_1)^2+(y_2-y_1)^2)`

Explanation:

Step 1: Define

Identify

Point (0, 0)

Point (-3, 5)

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 = √((-3-0)^2+(5-0)^2)`
2. [√Radical] (Parenthesis) Subtract:
   `\displaystyle d = √((-3)^2+(5)^2)`
3. [√Radical] Evaluate exponents:
   `\displaystyle d = √(9+25)`
4. [√Radical] Add:
   `\displaystyle d = √(34)`