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Missing something basic (Geometry)?

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by raj.may6 » Mon Apr 30, 2012 6:11 pm
Ref - OG (2nd edition ), Ques 102

Ques: In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k then x+y = ?

Though I got the question right but then I was trying to use different approach (rather, was testing slope definition) and kind of lost --

line is y = 2x

Now, (4-y)/(x-3) = slope = 2 ==> 4-y = 2x - 6 ==> 4 - y = y - 6 (as y = 2x) => 2y = 10 => y = 5, x = 5/2
This is not the answer but.
what am I doin wrong?
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by limestone » Mon Apr 30, 2012 6:33 pm
Hi,

I guess the prolem here is you just assume "x" and "y" in the points (3,y) and (x,4) the same with "x" and "y" in the line y= 2x.

Just let a and b substitute for x and y in the two points: (3,b) and (a,4). Note that this is nothing different than the two points (3,y) and (x,4) as a,b,x,y are all variances. Now how can you say b = 2*a ?
You just know that two above points are in the line y = 2x, then b = 3*2 = 6; a = 4/2 = 2. You can say b=2a only when the point (a,b) is belong to the line y=2x, but the given data only say (3,b) and (a,4) belong to the line.

Hope this helps.
"There is nothing either good or bad - but thinking makes it so" - Shakespeare.
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by raj.may6 » Mon Apr 30, 2012 9:24 pm
oh dear -- such a crap from me :)
thanks "limestone" --- probably this is what happens when you stretch to 5 hrs :)
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