How do I find the distance between two points?
user
You can use the Pythagorean Theorem to get the distance between the 2 points.

If this is in a 2d space you take the difference in the x axis and square it and you add that to the distance in the y axis squared. Then you take the square root of the total
for $(x_1,y_1)$ and $(x_2,y_2)$
$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
For 3d space you just add the third coordinate like this:
for $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$
$\sqrt{(x_2-x_1)^2+(y_2-y1)^2+(z_2-z_1)^2}$
assistant
Can you provide some example with actual numbers and include the steps?
user
Let's say you have two points, $(x1, y1)$ and $(x2, y2)$

Step 1: Calculate the difference between the two points for each coordinate:

$x2 - x1$

$y2 - y1$

Step 2: Square each of the differences from Step 1.

$(x2 - x1)^2$

$(y2 - y1)^2$

Step 3: Add the squared differences from Step 2 together.

$(x2 - x1)^2 + (y2 - y1)^2$

Step 4: Take the square root of the sum from Step 3.

$\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

Now, let's try this with some actual numbers. Suppose you have two points, $(3, 4)$ and $(6, 8)$.

Step 1: Calculate the difference between the two points for each coordinate:

$x2 - x1 = 6 - 3 = 3$

$y2 - y1 = 8 - 4 = 4$

Step 2: Square each of the differences from Step 1.

$(x2 - x1)^2 = 3^2 = 9$

$(y2 - y1)^2 = 4^2 = 16$

Step 3: Add the squared differences from Step 2 together.

$(x2 - x1)^2 + (y2 - y1)^2 = 9 + 16 = 25$

Step 4: Take the square root of the sum from Step 3.

$\sqrt{(x2 - x1)^2 + (y2 - y1)^2} = \sqrt{25} = 5$

So, the distance between the two points, $(3, 4)$ and $(6, 8)$, is 5.
assistant