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# M12-13

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Math Expert
Joined: 02 Sep 2009
Posts: 43312

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10 Sep 2017, 22:36
RekhaKulkarni wrote:
Hi, Can anyone tell me what will be the final equation of the line once we know what a and b are?

From a=-b and a-b=1, we can get that a = 1/2 and b = -1/2. So, we know that k passes through the point (1/2, -1/2) and is perpendicular to line y = 2x (slope = 2)

The two lines are perpendicular if and only if the product of their slopes is -1, so m*2 = -1 and m = -1/2 (the slope of line k).

Finally, the equation of a straight line that passes through a point $$P_1(x_1, y_1)$$ with a slope m is: $$y-y_1=m(x-x_1)$$. Substitute: $$y-(-\frac{1}{2})=-\frac{1}{2}(x-\frac{1}{2})$$ --> $$y = -\frac{x}{2} - \frac{1}{4}$$.

Check below:

For Coordinate Geometry check:

24. Coordinate Geometry

For more check:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.

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13 Sep 2017, 22:20
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. i read the whole thread, and still didn't understand the explanation. I do understand that we don't need to find the value of a and b, question is why would we discard 1） and 2) as insufficient, what's the reasoning behind it.

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13 Sep 2017, 22:32
d975490 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. i read the whole thread, and still didn't understand the explanation. I do understand that we don't need to find the value of a and b, question is why would we discard 1） and 2) as insufficient, what's the reasoning behind it.

(1) and (2) individually are insufficient for the same reason: different values of a and b satisfy each statement, giving different points of (a, b), thus giving different equations of line k that is perpendicular to line y = 2x.

For example, for (1), if x = 2 and y = -2, then the equation of line k would be y = -x/2 - 1 (apply the approach used HERE) but of x = 1 and y = -1, then the equation of line k would be y = -x/2 - 1/2. Two different answers, hence insufficient.

Hope it's clear.
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31 Dec 2017, 11:55
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Bunuel wrote:
Official Solution:

Notice that we can get the equation of line $$k$$ which is perpendicular to line $$y=2x$$ if we know ANY point that line $$k$$ passes through. So, to get the equation of line $$k$$ we need the values of $$a$$ and $$b$$.

(1) $$a = -b$$. Not sufficient.

(2) $$a - b = 1$$. Not sufficient.

(1)+(2) $$a = -b$$ and $$a - b = 1$$, we have two distinct linear equations with two unknowns so we can solve for $$a$$ and $$b$$. Sufficient.

Hi, Bunuel!

Is it necessary to find the equation of line in absolute values of 'a' and 'b'? I mean the point (a,b) is given. Can't we just take 'a' and 'b' as known values because point (a,b) is mentioned?
My first thought while solving this question was that slope is given and point (a,b) is given through which the line passes. Only 'c' is unknown to find the equation of line. Taking each of the statements one by one, i was able to find the value of 'c' in terms of 'a' or 'b' and hence the equation of line in terms of all the known values i.e 'a' and 'b' was obtained.
So, this way each statement was sufficient according to me and I thought D to be the answer.

Please, clarify my this doubt.Thank you.

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Re: M12-13   [#permalink] 31 Dec 2017, 11:55

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# M12-13

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