Very VERY Simple Math That's Confusing Me...

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HenryGifford
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Very VERY Simple Math That's Confusing Me...

Postby HenryGifford » Thu Nov 27, 2008 7:21 pm UTC

Studying for an Algebra test we have on Monday (I'm in Geometry but my Geometry teacher decided our Algebra teacher was bad and is teaching us a little Algebra so we can get the distance between a line and a point not on the line)

Anyway, I'm trying to get that so I made this problem

A line with an equation of:[math]y=(3/5)x+2[/math]
And a point not on the line (4, 1)
First drew the line between the point and the line perpendicular to the line and got this equation:[math]y-1=(-5/3)(x-4)[/math]
[math]y=(-5/3)x+(20/3)+1[/math]
[math]y=(-5/3)x+(23/3)[/math]
I set the two equal to eachother to get the intersection between the two lines so...
[math](3/5)x+2=(-5/3)x+(23/3)[/math]
[math](3/5)x+(5/3)x=(23/3)-2[/math]
[math](15/34) (34/15)x=(17/3)[/math]
[math]x=(85/34)[/math]
So I have for the point (85/34, y)

My only confusion is that the point I have is to the right of the original point (4,1) and has a smaller x.

Did I do incorrect math? When I plug in the x for both equations it comes out to the same thing, so it seems right. Maybe I just drew an incorrect picture?
Thanks.
Last edited by HenryGifford on Thu Nov 27, 2008 7:45 pm UTC, edited 2 times in total.

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thornahawk
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Re: Very VERY Simple Math That's Confusing Me...

Postby thornahawk » Thu Nov 27, 2008 7:27 pm UTC

Well the slope of the perpendicular ought to be -3/5, for starters...

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HenryGifford
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Re: Very VERY Simple Math That's Confusing Me...

Postby HenryGifford » Thu Nov 27, 2008 7:40 pm UTC

Sorry, the equation of the first line I wrote wasn't the one I had down on paper.
I really had:
[math]y=3/5x+2[/math]

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jaap
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Re: Very VERY Simple Math That's Confusing Me...

Postby jaap » Thu Nov 27, 2008 9:46 pm UTC

It looks ok to me.

HenryGifford wrote:[math]x=(85/34)[/math]So I have for the point (85/34, y)


x = 85/34 = 5/2
The y coordinate of that point on the line is 7/2.
That is to the left of (4,1), and the line goes upwards and to the right above the point (4,1).
At x=4, the line is at y=22/5, much higher than (4,1).

HenryGifford
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Re: Very VERY Simple Math That's Confusing Me...

Postby HenryGifford » Thu Nov 27, 2008 11:05 pm UTC

I saw my problem, I had merely plotted the point incorrectly. Stupid me.
Anyway, thanks for reducing that for me, I don't see why I hadn't seen the 17 in both of them. I didn't exactly mathematically draw the line... More a random sort of thing, and my teacher will (Hopefully) be better at plotting than I.


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