Let's do this question, find the center of the triangle whose vertices are five comma for zero comma
four and five, comma zero.
All right, pause the video, give it a try and then let's do it together.
All right.
We are back.
Let's do it together.
Let me draw the axis over here and let me get started by plotting these three points.
So this is zero comma for this is five comma four and this is five comma zero.
Let me join these vertices to get the triangle.
All right.
Now, we need to first find the length of the sites right over here.
You can see that this is a line.
Where would this point and this point has the same Y coordinate.
That's four and four.
Right.
So this line will be parallel to the X axis.
So I just need to find the difference between the X coordinates to find this length.
That's five minus zero.
So this length over here is five units.
And similarly, you can find that this length over here is four units, right.
Because it has the same X coordinates.
So this line is parallel to the Y axis.
And I just need to do for minus zero to find this length over here.
Now, after getting five over here and four over here, I can use Pythagoras Theorem right this length
over here will be a square root of PI squared plus four square.
That's equal to 41.
Right.
Root of 41.
All right.
Now, we have found the three sides of this triangle right now.
Remember, how do we find the center?
You need to multiply the length of the side with the corresponding coordinate of the opposite vertex.
That is to find the X coordinate of this.
In the center of this triangle, you need to multiply four with zero.
Right, because over here you have zero four into zero.
That's this year plus five in two.
Sorry, this five.
This five into this five.
Right.
So five to five.
That's this over here.
Plus root of 41 into this five over here.
So root for into five divided by A plus B plus that's five plus four plus Route 41.
Similarly to find the Y coordinate you need to multiply four with this, four over here.
That's four in the four plus five into this zero over here.
So five zero plus Route 41 into this four over here.
And then you need to divide it with A plus B plus there's five plus four plus Route 41.
And this is your answer.
And this simplifies to twenty five plus five, Route 41 by nine plus Route 41, comma 16 plus four,
Route 41 divided by nine plus Route 41.
And that is your answer.