MathChat

Friendly Formula: the Distance Formula

A few days ago I posted a “Friendly Formula” for the Midpoint Formula.

Today I am presenting a Friendly Formula for the Distance Formula, an important formula in Algebra 1 courses.

First I’m going to present the Friendly Formula for the Distance Formula and demonstrate how to use it. Then I’ll explain why it makes sense.

Buckle your seatbelts ’cause here it is: the distance between any two points on the coordinate plane is simply the SQUARE ROOT of …
(the x-distance squared) plus (the y-distance squared).

And here’s an example of how easy it can be to use this formula.
Suppose you want the distance between the points (2, 5) and (4, 9).

First figure out how the distance between the x-coordinates, 2 and 4.
Well, 4 – 2 = 2, so the x-distance = 2.
Now square that x-distance: 2 squared = 4

Next find the distance between the y-coordinates, 5 and 9:
Well, 9 – 5 = 4, so the y-distance = 4.
Now square that y-distance: 4 squared = 16

Next add the two squared values you just got: 4 + 16 = 20

Finally take the square root of that sum: square root of 20 = root 20.

That final value, root 20, is the distance between the two points.

Now we get to the question of WHY this Friendly Formula makes sense. I will explain that in my next post.

HINT: The Distance Formula is based on the Pythagorean Theorem. See if you can spot the connection.

EXTRA HINT: Make a coordinate plane. Plot the two points I used in this example, and construct a right triangle in which the line connecting these two points is the hypotenuse. If you can figure this out, the “Aha!” moment is a glorious event!