Tutorial: Distance Formula

Question

calculusxy · Answer

Distance Formula
The distance formula is essential when finding out the distance between two points. The formula derives from the Pythagorean Theorem. (The derivation will be shown at a later time.)

$\large D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2)}$

The $x_1, x_2, y_1,$ and $y_2$ values are found from the coordinates of the two points.

**Note: It does not matter whether the first coordinate will have their x- and y-values be designated with $x_1$ and $y_1$. But one must be cautious about making sure that whatever coordinate of the two has its x-coordinate take the value of $x_1$, then that coordinates y-coordinate must take the value of $y_1$. That makes the other coordinate have their x- and y-values have the coordinates of $x_2$ and $y_2$.**

Example Problem
Find the distance between the coordinates (1, 2) and (4, 6).

Let’s make the x- and y-values of the coordinate (1, 2) be designated with $x_1$ and $y_1$. Therefore, the x- and y-values of the coordinate (4, 6) will be designated with $x_2$ and $y_2$. So we have: 
$x_1 = 1$ 
$y_1 = 2$
$x_2 = 4$ 
$y_2 = 6$

Substitute those values into its corresponding areas in the distance formula. 
$\large D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2)}$ 
$\large D = \sqrt{(4 - 1)^2 + (6 - 2)^2)}$
$\large D = \sqrt{(3)^2 + (4)^2}$
$\large D = \sqrt{9 + 16}$
$\large D = \sqrt{25}$ 
$\large D = 5$ 
Answer: The distance between the coordinates (1, 2) and (4, 6) is 5 units.

Ultrilliam · Answer

Would you like me to re-open this for you?

calculusxy · Answer

That would be great! @Ultrilliam

Ultrilliam · Answer

re-opened :)

Ultrilliam · Answer

Annnd it's closed again?

calculusxy · Answer

I didn't touch the closed option at all.