Let's do this question, find the center of the triangle whose vertices are zero zero zero and six eight.
All right, boss, the video, give it a try and then let's do it together.
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We're back.
Let's do it together.
Let's draw our triangle over here.
So the vertices are given as zero zero six comma eight and 10 zero.
Right.
Let this be all A and B..
Now, the altitude through all and perpendicular to Ebe, can you find the equation of the altitude
through old and perpendicular to remember.
That's what we need to do, right.
We need to find two altitude and then we need to find the point of intersection of those two altitudes.
All right.
But let's get started by finding the altitude through and perpendicular to Ebby.
Now the equation of a nine through zero zero would be Y is equal to mix, right.
Because it's passing through the origin so it does not have it y intercept.
Now what is the slope of line?
We know we can find the slope by digging Y to minus Y one divided by x2 minus X one.
Right.
Therefore the slope of a B would be eight minus zero divided by six minus 10.
That's equal to.
Eight divided by minus four, which is equal to minus two, right?
Therefore, if the slope of a B over here is minus two, then the slope of the altitude has to be one
by two.
Right.
So the equation of the nine.
That's true.
And it's perpendicular to a B or the altitude two is equal to Y is equal to one by two X.
Now why is this equal to one by two because one by two in two minus two gives you minus one.
Remember M1, M2, where M1 and M2 are slopes of two lines that are perpendicular as to be equal to
minus one.
That's why, because this is minus two, minus two in the M2 is equal to minus one and hence M2 is equal
to one by two.
Right.
That's how we got this over here.
All right.
Let me make some space over here.
Now let's find one more altitude and then we can find the point of intersection.
Now, what is the slope of line or B, that would be eight divided by six, right?
That's eight minus zero.
Divided by six minus zero.
That's equal to it by six or four by three right now.
If you want to find the line that is perpendicular to or B.
Right.
And it passes through if that's what we are trying to find out.
Let me write that over here.
That would be Y is equal to minus three by four X plus.
See the general equation, because over here the slope is four by three.
So the slope over here has to be minus three by four right now.
Substitute ten comma zero into this line because it's passing through point eight.
Now, when you do that, you will get zero is equal to minus three by four in 10 policy.
That gives you the value of C, right.
That C would be three by four and 210.
Right.
All right.
Let's take this aside.
And hence the equation of the altitude through a and perpendicular to or B is equal to why is equal
to minus three by four X plus fifteen by two.
Right.
So this simplifies to fifteen by two.
Right.
All right.
Now you have one already over here and the other altitude over here.
So you just need to find the intersection of these two lines.
So let's substitute Y as explained to over here to explain two is equal to minus three by four X plus
fifteen by two or five by four.
X is equal to fifteen by two or you get X is equal to six right now when X is equal to six to subscript
over here, Y has to be six by two.
That's why is equal to three.
Therefore six comma three is the point of intersection of these two altitudes.
That is six comma three is the auto center.