Let's do this question, find the distance between the centroid and sock'em center of a triangle with
coordinates 12 comma zero zero, comma 12 and 12 12.
All right.
Also, we will give it a try and then let's do it together.
Remember to start by plotting the points.
All right.
We are back.
I hope you have given it a try.
Let's do it together.
So I have my access over here.
Now, let me plot the three points.
So this is 012.
Is this 12, comma 12 and this is 12 comma zero.
Let me join the points together and you can see that you are getting it right angled triangle right
now.
Therefore, the circle center is that midpoint of the hypotenuse.
Right.
Because we have seen that in the case of the right angle triangle, the circle center is the midpoint
of the hypotenuse.
And over here, this side is the hypotenuse.
Therefore we get the circumstances zero plus twelve by two comma, twelve plus zero by two, right where
you have zero.
And this is 12.
That's why zero plus twelve by two.
Similarly of twelve over here and zero over here to 12 plus zero by two to the sock'em center is six
comma six.
All right.
Now we know how to find the centroid, right.
We just need to add all the coordinates and divide by three.
And similarly, we need to add all the Y coordinates and divide by three.
To the center of this triangle is zero plus 12 plus 12 by three, comma 12 plus 12, plus zero by three
zero 12 and 12.
That's over.
We're here in 2012 and zero that's over here.
Now this gives the centroid as twenty four by three comma.
Twenty four by three.
That's equal to eight comma eight.
Now we have found the centroid and the sock'em center and we are asked to find the distance between
these two points.
Now we know how to find the distance between two points that would be square root of eight minus six,
the whole square plus eight, minus six, the whole square that's root of two squared plus two square,
which is equal to to rule two.
And that is your answer.