Welcome back. This time we're going to find the distance between given two points and the coordinate of the midpoint of the line segment between two points. So as you see, there are two points are given.
So negative 2 and negative 4 and 1, 5. So the first step, I want to plot those two points on the plane graph. So as you see, negative 2 and negative 4 are given. 4 will be here and 1 and 5 is right here.
Okay so let me do the line segment between these two points. Then this line become like that and we want to find out the distance of these two points. So simply, we can think this way. So let me draw these two more lines.
One of the vertical line which passing through x equal to 1 right here. And the other segment I'm passing through negative 4 here. Then as you see, we make one vertical and then one horizontal. So this angle become 90 degree and this new point we can say 1, negative 4 here.
So let me label all these points. So this is the negative 2, negative 4 and this become 1, 5 here. So it looks really familiar.
It is right triangle. and the right triangle then we can using PWM theorem and find the hypotenuse and this time this line segment this line segment that represent the distance here so we can say this is c or d here distance between these two point okay so before we finding d Let's figure out distance between two axes and distance between two y's. So from this point to this point, what's the measurement here?
So as you see, we can make one, two, three units. But look carefully here. When we make 3 units, we making is from negative 2 and then we reach on the 1 here.
Therefore, we have difference between two x values here. So that is called delta x. Okay, now similarly, these two point.
So difference between these two lengths will be total become 1, 2, 3, 4, 5, 6, 7, 8, 9. That becomes our delta y. So far we can find delta y equal to 9 and delta x equal to 3 here. Okay. Therefore, we can find out distance t using the fifth-dynamic theorem from now on. So Using d squared equal to so basically Delta x squared plus Delta y squared So we know Delta x equal 3 and Delta y equal to 9 therefore d squared equal to 3 squared plus 9 squared So this becomes d squared equal to 9 plus 81. So if you calculate that, d squared becomes 90. So final step, we take a square root so that we can find d value here.
And d equal to root 90. Let's simplify using the prime factorization. Then as you see, 9d equal to 9 times 10. We know root 9 become 3. Therefore, d become 3 root 10 here. So, we found... a answer, first one answer, so distance between these two points will be 3 over 10 here.
But before moving on next question, then let's think about you know how we can compose as a formula here. So when we find out this one, how to find delta x? We need to find out what it means clearly. So delta x case, as I told you, a difference measurement from first point to second point here. So we already know delta x means difference between two axes.
Then same concept, delta y must be difference between two y's. Therefore, now we can make delta x, I can say, in this case, 1 minus negative 2. Delta y equal to 5 minus negative 4 here. Now, but what about other cases? This case, we have two fixed points, negative 2 and negative 4, and 1 and 5. That's why delta x set up becomes like that. But why don't we have maybe random points?
Then how can we figure out distance? So, I'm going to set up x1, y1, and x2, y2. Then, delta x will be x2 minus x1, and then delta y will become y2 minus y1.
And we know that the Pythagorean theorem, d squared, equal to delta x squared plus delta y squared. Another word, we can rewrite that, d squared equal to x2 minus x1 squared because that means delta x plus y2 minus y1 squared here. So later on, we will make square root so that we can find distance as d, not d squared. So we can make d equal to square root x2 minus x1 squared plus y2-y1 square.
So that becomes actually distance formula. Okay then let's plug the given point into this formula and then find the distance. So d equal to square root. So in this case you can name x1 y1 and x2 and y2 so any order. So now I'm gonna name that x1, y1, x2, y2.
Then this becomes 1 minus negative 2 squared plus 5 minus negative 4 squared. So d becomes square root total 3 squared plus 9 squared. So this becomes 9 plus 81 equal to root 90. So, d equal to 3 root 10. If you look at this video, distance formula actually from the PWM theorem. But to make it easier, without drawing triangle, without drawing the plane graph, we can use that formula and from now on, you can find the distance.
between two points. Thank you.