How Was the Distance Formula Derived?

Note:

Trying to find the distance between two points on the coordinate plane? Use the distance formula! Can't remember it? Not a problem if you've watched this tutorial! This tutorial shows you how to derive the distance formula. You even use the Pythagorean theorem to find it! Take a look!

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Background Tutorials

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
- What is a Line Segment?
  
  A math term can really tell you a lot about the thing it's describing. Take the term line segment. A line segment is just part of a line! In this tutorial, learn about line segments, how to name them, and what the midpoint of a line segment is!
- What are Acute, Obtuse, Right, and Straight Angles?
  
  Did you know that there are different kinds of angles? Knowing how to identify these angles is an important part of solving many problems involving angles. Check out this tutorial and learn about the different kinds of angles!
Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
- What are Acute, Obtuse, and Right Triangles?
  
  Did you know that there are different kinds of triangles? Knowing how to identify these triangles is an important part of solving many problems involving these triangles. Check out this tutorial and learn about some of the different kinds of triangles!
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- What is the Coordinate Plane?
  
  You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.
- What is the X-Coordinate?
  
  Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the x-coordinate in an ordered pair!
- What is the Y-Coordinate?
  
  Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the y-coordinate in an ordered pair!
- What is the X-Axis?
  
  To graph a function or plot an ordered pair, you need to use a coordinate plane, so you should learn all about it! In this tutorial, you'll learn ab
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).
- How Do You Evaluate an Algebraic Expression?
  
  Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.
Explain a proof of the Pythagorean Theorem and its converse.
- What is the Pythagorean Theorem?
  
  The Pythagorean theorem is a very popular theorem that shows a special relationship between the sides of a right triangle. In this tutorial, you'll get introduced to the Pythagorean theorem and see how it's used to solve for a missing length on a right triangle!
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
- What are the Legs and Hypotenuse of a Right Triangle?
  
  Looking for some terminology used with right triangles? Then this tutorial was made for you! In this tutorial, you'll be introduced to the names for the different parts of a right triangle. Check it out!