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

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HenryGifford
Posts: 152
Joined: Mon Nov 03, 2008 2:01 am UTC

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

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.

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

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

~ Werner

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HenryGifford
Posts: 152
Joined: Mon Nov 03, 2008 2:01 am UTC

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

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

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

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
Posts: 152
Joined: Mon Nov 03, 2008 2:01 am UTC

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

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.