Question 1

who came up with this formula?

Accepted Answer

The distance formula is a consequence of the Pythagorean Theorem.

Question 2

POV: your teacher makes you show your work

Accepted Answer

The worst feeling in the world is when you lose a point because you "Didn't show your work" like. Ow

Question 3

bro why do we have to do this

Accepted Answer

I cannot say why you have to, but I can say why this might be useful in the future. 
Lets say for whatever reason you needed to make a video game, and let’s also say you needed to calculate the distance between a player and an object in order to make an action occur. I imagine this would be useful for those purposes

Question 4

I still don't understand any of this... :I

Accepted Answer

I haven't read any of the article on this so I really hope I don't say the exact same thing he says.... here goes:

Here is the graph I am referring to in my explanation: https://www.desmos.com/calculator/juthaysfbl
-- only look at the graph, ignore everything on the sides and bottom --

(intuitive solution, and how I learned this)

Think of the Pythagorean theorem. The formula is a^2 + b^2 = c^2 . Now, imagine two points, let's say they are (0,0) and (3,4) to keep it simple. Look at the blue line going from (0,0) to (3,0). This is the base, with a distance of 3 units. How did we find this? We took one of the x values (3) and subtracted it by the other (0). 3 - 0 = 0. Next, we must find the height. The red line represents it, and it is a length of 4 units. We found this, again, by subtracting the y values (4 - 0 = 0). We can now find the hypotenuse, if we replace a and b with the base height length, so we get 3^2 + 4^2 = c^2 (where c is the orange line, or hypotenuse). The hypotenuse is the distance of the two points.

Of course, we can square root both sides so we get c = sqrt( 3^2 + 4^2). We can expand this even further if we replace the 3 and 4 with how we got there, so c = sqrt( (3 - 0)^2 + (4 - 0)^2). But what do 3 and 0 and 4 and 0 mean? The two x values and y values, respectively. Therefore, we replace the numbers so we get c (hypotenuse) = ( ( x1 - x2) ^2 + (y1 - y2) ^2) .

I really hope this helped you, I spent a long time explaining this lmao...

Question 5

how is the formula the same as the Pythagorean theorem

Accepted Answer

The x and the y axis are perpendicular, so if you imagine a right triangle when you find a distance, and the hypotenuse is the distance

Question 6

okay I understand all you have to do is take your y axis and divide it by your x axis

Accepted Answer

If you were to get two perfect squares under the giant square root after subtracting the two points within each parentheses, would you be able to separate them in order to pull them out of the square root and make them rational? 
For example, if I got "the square root of (6)^squared + (6)^squared" would I first square them and get "the square root of 36+36?" or could I separate them into "the square root of 36 + the square root of 36"

Question 7

I don't get it and I have a test tomorrow it's hard for sixth grade

Accepted Answer

I most likely responded wayyyy to late for this, but I thoroughly recommend you go through both the article and video ( maybe the practices!) and study hard.

Question 8

Sooooo, if I have two points, (1, 2) and (-1, 4), it does not matter in which order I subtract as long as I do the x with the x, and so on? Because it doesn't look that way.

Accepted Answer

when you square a negative it becomes a positive

Question 9

what is the formula that is used to find distance between two points

Accepted Answer

bro are u crazy its right above you in the beginning of the lesson

Course: 8th grade > Unit 5

Distance formula

Deriving the distance formula

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