Distance In Math
There are many different ways to determine the distance between two objects. And, 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.
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 does not matter which point is (x1, y1) or which one is (x2, y2) - just as 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.
Examples
1.) Find the distance between the given points:
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The coordinates of the two points are:
(x1, y1) = (2, 5)
(x2, y2) = (9, 8)
Then, to solve, you just need to substitute the numbers into the distance formula.
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.
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For this example, the points are
(-1, 2) and (2, 1)
When using the distance formula with negative numbers, it is very critical to work carefully so you don't lose the negative along the way.
d = ?(2 - (-1))^2 + (1 - 2)^2
d = ?(3^2 + (-1)^2)
d = ?(9 + 1)
d = ?(10)
d = 3.2
If you are 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:
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Since the points are in a straight line, it is easy to count the distance between them and get the answer, which is 3. Let's use the distance formula as well to prove our answer.
d = ?(x2 - x1)^2 + (y2 - y1)^2
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