High students in this video, let's learn how to find the distance between two points in the X Y plane.
All right, over here, I have the access.
OK, and let's take two points.
That's point A and point B now point it has X, coordinate X and Y, coordinate wyvern and point B has
X, coordinate x2 and Y coordinate Y to.
Now we are trying to find the distance between a B that is the length of the nine segment A B now the
distance between and B is given by the formula D equal to square root of x2 minus X one, the whole
squared plus Y to minus Y one.
The whole square.
First, let's try to find the link between these two points and then we'll discuss why this formula
is correct.
All right.
Now over here, we know that this is one and this is two.
So let's take it as one, two.
And similarly, let's take B.S. six, five.
All right.
Now let's try to find this distance between them.
Let's plugging these values into this equation so we get these equal to square root of six minus one,
the whole square.
Right.
This is six and this is one and five.
Minus two.
That's five.
And this is two.
The whole square.
Now, it does not matter which one you take us one and which one you take us to.
Right.
Because we are taking the square.
So even if you take one minus six and take the square, it'll still be twenty five and six minus one.
The whole square is also twenty five.
So the distance is equal to square root of five squared plus three square and that gives you square
root of thirty four.
All right.
Now you can see that this equation over here is on the basis of the Pythagoras theorem right now.
Why is that so.
Let me draw this over here.
OK, so you can see that over here you get the right angle triangle right now, what are the lengths
of these sides?
This side over here will be wide to minus Wyvern.
Right over here you have five and this is two to five.
Minus two gives you three.
So this side is of length three.
That's the three you have over here.
And what about this over here, the extraordinary six.
And over here, the X coordinate is one.
So you have this length is six minus one.
That is what you have over here, right?
That's the five over here.
That's why the distance between two points is given by this formula.
That is a square root of X2, minus one, the whole square plus Y to minus Y one.
The whole square.