If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region?

(A) 5
(B) 10
(C) 25
(D) 50
(E) 100


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explaination given
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The end point of the square are (0, 5) (5, 0) (0, -5) (-5, 0); each side of the square equals to and the area of the figure is that expression squared or 50.

How do I know the enclosed region is square ?? Also can anyone please elaborate on the explaination. I did not understand.

Edited by: GT

given equation |x| +|Y| =5

|y|= -|x|+5

if x=0 then the points are (0,-5) & (0,5)
if y=0 then the points are (5,0) & (-5,0)

note : since we are dealing with absolute values there is 2 possible values


plotting the above 4 points you will get 4 right triangles or a single square


area of 1 right triangle = 1/2*5*5

area of 4 right trianlges = 4*1/2*5*5 = 50

so ans is D

All sides are equal and perpendicular to each other. Therefore it is a square.

Puneet,

No where it is said that sides are equal to begin with, though they are on coordinate axes.

anyway I am not fretting on this one anymore.. thanks folks

-Mo

>How did u know the pts on the basis of which you made the graph?

Please explain this problem from the scratch as my coordinate geometry+graphs knowledge is absolutely nil.
much appreciated.
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countdown-beginshas-ended-85483-40.html#p649902

its a tricky one but really easy....points to note in this question are
1) The degree of equation is 1 therefore relation between y and x is 'linear' ( straight line )
2) This question involves |x| and |y| instead of x,y so its obvious that it demands to consider negative values as well

Approach:


1) Going by the equation, we need values of x and y such that their sum is 5.
2) find pair of (x,y) which will total 5 .......(0,5) ...also, as its a |y| and not y....therefore (0,-5) also satisfies the equation ......Mark these points
3) Now, consider x coordinate ....(5,0) and (-5,0) for the reason stated above [ imp note, we are trying to find the restrictions of the region...the boundary, if to put it bluntly]
4) Now you have 4 points, (0,5) (0,-5) (5,0) (-5,0) ......
5) Join these points with a straight line and form the diamond shape figure as shown in the post above
6) The reason why we join the points with a straight line is because the degree of equation is 1 and relation between x, y is linear ( y+x = 5 therefore slope of line is -1 )
7) easier alternative to point6 is by substituting values...example, by plotting other pairs are (1,4) (2,3), (3,2) etc etc ....we get the same shape

even if we consider decimal numbers ( 0.9, 4.1) then also the linear relation does not change.


i hope it helps.....let me know if u have any doubt

by the way, so the answer is 50 .....how?? .....4 times the area of one triangle....[ 4X ( 1/2X5X5) ]

I understand how the answer is D. But why are we picking extreme values (5,0), (-5,0) etc in this question? I tried using values (2.5,2.5), (-2.5,2.5) etc as they add up to 5 taking the absolute value into account. This made me think this is an equation of a circle (since the coordinates will always be equidistant from the origin) and I applied the formula for area of circle and got wrong answer (Although the square can cover a circle satisfying the equation in question, the equation is clearly not that of a circle).

My question is whether in questions around absolute values in geometry, it is a thumbrule(at least in some cases) to get the x and y axis intersection points for calculation ?We only need to connect the lines and get to know the exact shape after doing this. The solution does not mention why the extreme values are taken in the first place.

Ideas anyone ?

Hi Intcan,
please can you make reference to the OG question?
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KUDOS me if you feel my contribution has helped you.

Can ne one suggest sm gud book for coordinate geometry!!!

All these points would be on the square. But there are infinitely many points that satisfy the equation (for example, (1, 4), (1.2, 3.8), ...) and all these points will result in square.

Go through the following post for a solution, theory and similar questions: m06-q5-72817.html#p1032170

Hope it helps.
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