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Let's do this question, find the coordinates of the foot of the perpendicular from three comma five

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to the nine X plus two is equal to eight.

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All right, what does it mean?

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We have a different line that this line B, the given line X plus two is equal to.

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Now we have a point three comma five.

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Now we need to draw a perpendicular from three five to this line.

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But this angle over here is 90 degrees.

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And we need to find this point, OK, to pause the video, give it a try, and then let's do it together.

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All right.

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We are back.

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Let's start finding the equation of this line over here.

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That is the line that is perpendicular to the given line.

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Now, over here, the given line is two way plus X, minus eight is equal to zero.

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Right now, we can write the equation of this line that is perpendicular to the given line as Y minus

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two explosive is equal to zero.

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Right.

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All we did is we interchange the coefficients and we change the sign over here.

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Now we know that this line, that is this line over here passes through three comma five.

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Right.

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So let's substitute three comma five into this equation.

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All right, so that gives us five minus two in the three plus CS equal to zero, right.

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And hence C is equal to one.

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All right.

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So the equation of this line over here is Y minus two, X plus one is equal to zero.

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Right now, we know that this line and the initial line with which we started off intersect at this

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point, which is the point that we are trying to find.

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So let's try to solve between this equation and this equation for that.

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Let's multiply this equation with two.

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So I get to a minus four, X plus two is equal to zero.

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Right.

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And the given equation is to Y plus X minus eight is equal to zero.

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So let me subtract these two equations or two and minus two is equal to zero minus four X minus gives

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me minus five X and two minus minus eight gives me 10 to minus five X plus ten is equal to zero or X

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is equal to two.

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All right.

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Now substituted into the given equation and you get Y is equal to three.

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Right.

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Therefore the point of intersection is to come up three.

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Now let's discuss one more method in which we can solve this question.

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Let me make some space over here now.

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We will see this other method.

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So this is a given nine X plus two is equal to eight and we have three come on five, which is this

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point right now.

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We are dropping a perpendicular and we need to find the coordinates of a comma.

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Maybe that's the question right now.

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What would be the slope of this line?

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We know how to find the slope.

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If you have two points, the slope of this line will be B minus five, divided by A minus three.

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So this is the slope of this line and the slope of the given line over here is minus one by two.

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Right.

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Therefore, this slope over here has to be equal to two.

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Right, because these are perpendicular.

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So when you multiply them, you should get minus one.

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Now let's solve this.

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So you get B minus five is equal to A minus six.

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That gives to A minus B is equal to one, right?

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So we have this equation now as A and B is on this line over here, we can substitute it into the given

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line.

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Also right now on substitution, you will get A plus two.

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B is equal to eight.

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Right.

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So, again, you have two variables and you have two equations.

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You can solve it by multiplying this equation throughout with two and you will get B, and so by substituting

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back, you will get A and you will get the same answer.

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That is on solving.

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You'll get the point about two, comma three.

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And that is the answer to this question.