Distance in Math: Formula & Concept

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  • 0:03 Distance Formula in Math
  • 0:45 Distance Examples
  • 2:47 Origin of the Distance Formula
  • 4:16 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Distance is a numerical description of how far apart two objects are. This lesson describes the mathematical formula for determining distance and gives some examples.

Distance Formula in Math

There are many different ways to determine the distance between two objects. In addition, there are just as many tools that you can use. Mathematically, if you want to determine the distance between two points on a coordinate plane, you use the distance formula.

d = √(x2 - x1)^2 + (y2 - y1)^2

When you know the coordinates of the two points that you're trying to find the distance between, just substitute them into the equation. It doesn't really matter which point is (x1, y1) or which one is (x2, y2) - just so long as you keep them together. Whichever set you use for 1, use it for both x1 and y1, and whichever set you use as 2, use both x2 and y2 from that set.

Distance Examples

1.) Find the distance between the given points on this graph:


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The coordinates of the two points are:

(x1, y1) = (2, 5)

(x2, y2) = (9, 8)

To solve this equation, you just need to substitute the numbers into the distance formula that we looked at earlier. From there, all you have to do is simplify:

d = √(9 - 2)^2 + (8 - 5)^2

d = √(7^2 + 3^2)

d = √(49 + 9)

d = √(58)

d = 7.6

2.) Find the distance between the two points on the graph:


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For this example, the points are

(-1, 2) and (2, 1)

When using the distance formula with negative numbers, it's very important to work carefully so you don't lose the negative along the way.

Let's plug in our values to the distance formula and then simplify, just like before:

d = √(2 - (-1))^2 + (1 - 2)^2

d = √(3^2 + (-1)^2)

d = √(9 + 1)

d = √(10)

d = 3.2

If you're trying to determine the distance between two points that are on a straight horizontal or vertical line, you can just count the number of spaces between the points. The distance formula will work as well; however, the possibilities for error increase as well.

3.) Find the distance between the two points on this next graph:


Example 3 Graph


Since the points are in a straight line, it's pretty easy to count the distance between them and get the answer, which is 3. But, let's use the distance formula as well to prove our answer.

The two points on the graph are (1,6) and (1,3)

d = √(1-1)^2 + (6-3)^2

d = √(0)^2 + (3)^2

d = √(0+ 9)

d = √(9)

d = 3

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