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gmatprep coordinate geometry

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by resilient » Mon Apr 28, 2008 11:30 pm
In the xy coordinate system, if (a,b) and (a+3, b+k) are two points on the line defined by the equation x=3y-7, then k?


a.9
b.3
c.7/3
d.1
e.1/3

qa is d? IM confused because I plugged this into slope formula y2-y1/x2-x1 and got 7 for k. hmmm Im not seeing this. Can anyone help?
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by amitansu » Tue Apr 29, 2008 1:57 am
D is the correct ans.

Both the coordinate points must lie on this line.
so by putting their values separately can lead us the answer.

i.e. put (a,b) on the equation you would get : a=3b-7
so by putting the other point (a+3, b+k) we get :

a+3=3(b+k)-7
=> a=3b+3k-10
now comparing with 1st equation : 3k-10=-7
and k=1

Hope this clears the doubt.
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by AleksandrM » Tue Apr 29, 2008 1:18 pm
You can also rewrite the equation into the form of y = mx + b. Therefore:

y = x/3 + 7/3 the slope is 1/3

Now calculate the slope from given points.

(a,b) where a is x1 and b is y1

(a + 3, b + k) where a + 3 is x2 and b + k is y2

slope = y2 - y1/x2 - x1

slope = b + k - b/a + 3 - a
slope = k/3

Since both of the points lie on this line and the slope of this line is 1/3, then k/3 tells you that k = 1.
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excellent

by resilient » Wed Apr 30, 2008 7:21 pm
THank you guys for the help! ALeksander, i notice that you always think the way I think in re to math. I saw my mistake, I set the slope equal to 7/3 (y interecept) I should have nailed that question. Thanks for everything!
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