Deriving and Using the Distance Formula

Hello! For today's video, I will talk about the distance formula. In math, there are just an endless amount of formulas that we should memorize but sometimes the best way to memorize the formula is to understand where it comes from. One of the most important formulas that you should remember is the Pythagorean Theorem.

Pythagorean Theorem: a^2 + b^2 = c^2

Well, would you believe me if I said the distance formula is actually derived from the Pythagorean Theorem.

Distance Formula: d = sqrt [(x2-x1)^2 + (y2-y1)^2]

The formula looks quite different for now but in the first half of the video, I show you how the distance formula is derived from the pythagorean theorem. In a right triangle, we have each side represented by a, b, and c. The distance between two points can always be represented by a right triangle where the hypotenuse c would be the distance we are looking for. a would be represented as the horizontal difference between the two points (x2-x1) and b would be represented as the vertical difference between the two points (y2-y1). Anyways, let's take a look at the video!

Sections in the video:
0:00 Introduction to the Distance Formula
2:03 Deriving the Distance Formula from the Pythagorean Theorem
8:30 Practice Problem #1
10:45 Practice Problem #2
12:37 Practice Problem #3

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