Math Is Fun Forum

Radhika

Member

Registered: 2006-11-01

Posts: 2

Find the area

1)Sketch the graph of { (x , y) / | x+y|  + | x – y |  = 4 } and find its area.

fgarb

Member

Registered: 2006-03-03

Posts: 89

Re: Find the area

I'll get you started with the basic idea. Generally when you have these absolute value problems you should start by isolating one of the absolute terms, and thinking about just one at a time. In your case, we have:

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There are two possibilities for x+y: it can either be negative or positive. If it is positive the absolute value changes nothing and we can just take it away like this:

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Or it could be negative. In that case |x+y| = -(x+y), so you can substitute that in:

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These two equations describe different sets of points, but when you take them both together you get the same points as in the original equation with two absolute values. So you really can use these two equations in place of the one before. We started with one equation for the points in this graph, and by removing an absolute value we ended up with two equations for two different parts of the points that satisfy this graph. There is now one absolute value left in each equation. You can remove it in the same way as before and each equation will split into two more giving you four total equations that, taken together, specify the same set of points as the one original equation with two absolute values. Does that make sense?

Once you have all four equations try sketching the graph. It should be pretty obvious how to find the area of the result, but please ask if you get stuck.

Last edited by fgarb (2006-11-01 21:49:10)