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Let's do this question, find the center of the triangle whose vertices are zero zero zero and six eight.

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All right, boss, the video, give it a try and then let's do it together.

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All right.

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We're back.

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Let's do it together.

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Let's draw our triangle over here.

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So the vertices are given as zero zero six comma eight and 10 zero.

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Right.

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Let this be all A and B..

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Now, the altitude through all and perpendicular to Ebe, can you find the equation of the altitude

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through old and perpendicular to remember.

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That's what we need to do, right.

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We need to find two altitude and then we need to find the point of intersection of those two altitudes.

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All right.

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But let's get started by finding the altitude through and perpendicular to Ebby.

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Now the equation of a nine through zero zero would be Y is equal to mix, right.

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Because it's passing through the origin so it does not have it y intercept.

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Now what is the slope of line?

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We know we can find the slope by digging Y to minus Y one divided by x2 minus X one.

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Right.

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Therefore the slope of a B would be eight minus zero divided by six minus 10.

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That's equal to.

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Eight divided by minus four, which is equal to minus two, right?

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Therefore, if the slope of a B over here is minus two, then the slope of the altitude has to be one

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by two.

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Right.

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So the equation of the nine.

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That's true.

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And it's perpendicular to a B or the altitude two is equal to Y is equal to one by two X.

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Now why is this equal to one by two because one by two in two minus two gives you minus one.

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Remember M1, M2, where M1 and M2 are slopes of two lines that are perpendicular as to be equal to

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minus one.

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That's why, because this is minus two, minus two in the M2 is equal to minus one and hence M2 is equal

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to one by two.

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Right.

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That's how we got this over here.

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All right.

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Let me make some space over here.

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Now let's find one more altitude and then we can find the point of intersection.

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Now, what is the slope of line or B, that would be eight divided by six, right?

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That's eight minus zero.

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Divided by six minus zero.

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That's equal to it by six or four by three right now.

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If you want to find the line that is perpendicular to or B.

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Right.

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And it passes through if that's what we are trying to find out.

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Let me write that over here.

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That would be Y is equal to minus three by four X plus.

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See the general equation, because over here the slope is four by three.

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So the slope over here has to be minus three by four right now.

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Substitute ten comma zero into this line because it's passing through point eight.

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Now, when you do that, you will get zero is equal to minus three by four in 10 policy.

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That gives you the value of C, right.

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That C would be three by four and 210.

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Right.

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All right.

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Let's take this aside.

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And hence the equation of the altitude through a and perpendicular to or B is equal to why is equal

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to minus three by four X plus fifteen by two.

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Right.

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So this simplifies to fifteen by two.

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Right.

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All right.

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Now you have one already over here and the other altitude over here.

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So you just need to find the intersection of these two lines.

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So let's substitute Y as explained to over here to explain two is equal to minus three by four X plus

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fifteen by two or five by four.

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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

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over here, Y has to be six by two.

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That's why is equal to three.

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Therefore six comma three is the point of intersection of these two altitudes.

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That is six comma three is the auto center.