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11 Jun 2006, 19:12
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How do we solve the equation |x| + |y| = a (a is a positive integer)
I remember having done this long back and it intercepts a square(?) on the X-Y plane or some such, but my brain is a bit rusty now
Any help would be welcome.
~Pranay
I remember having done this long back and it intercepts a square(?) on the X-Y plane or some such, but my brain is a bit rusty now
Any help would be welcome.
~Pranay
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
15 Jun 2006, 17:56
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Let me try:
|x| + |y| = a;
The question is to find the area of the figure that is formed by this equation.
To start with, we need to break the above down into all possible forms. As you can see, by putting + and - signs before x and y, we get 4 possible equations.
1. x + y = a;
2. x - y = a;
3 -x + y = a;
4. -x -y = a;
Further, these all fall into the form of y=mx + c (the equation for a straight line). Also note that lines 1 and 4 are parallel and lines 2 and 3 are parallel by virtue of having the same slope.
Next, find out where these lines hit the x and y axes.
1. (0,a) and (a, 0)
2. (0, -a) and (a,0)
3. (0, a) and (-a,0)
4. (0, -a) and (-a, 0)
If you plot the points above, you can see its a square, where half the diagonal is of length a.
From here you can find the area of the square.
|x| + |y| = a;
The question is to find the area of the figure that is formed by this equation.
To start with, we need to break the above down into all possible forms. As you can see, by putting + and - signs before x and y, we get 4 possible equations.
1. x + y = a;
2. x - y = a;
3 -x + y = a;
4. -x -y = a;
Further, these all fall into the form of y=mx + c (the equation for a straight line). Also note that lines 1 and 4 are parallel and lines 2 and 3 are parallel by virtue of having the same slope.
Next, find out where these lines hit the x and y axes.
1. (0,a) and (a, 0)
2. (0, -a) and (a,0)
3. (0, a) and (-a,0)
4. (0, -a) and (-a, 0)
If you plot the points above, you can see its a square, where half the diagonal is of length a.
From here you can find the area of the square.
16 Jun 2006, 21:59
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Bookmarks
Thank you.
~Pranay
~Pranay
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
