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M06#5 Absolute value [#permalink]
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23 Jan 2011, 20:37
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If equation X + Y= 5 encloses a certain region on the coordinate plane, what is the area of that region? 5 10 25 50 100 The end points of the square are (0, 5) (5, 0) (0, 5) (5, 0); each side of the square equals and the area of the figure is that expression squared or 50. You can also find the area of a square by multiplying its diagonals by each other and dividing by 2. For example: .
The correct answer is D. How do we know that the area is square and not something else ?
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Re: M06#5 Absolute value [#permalink]
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shrive555 wrote: If equation X + Y= 5 encloses a certain region on the coordinate plane, what is the area of that region? 5 10 25 50 100 The end points of the square are (0, 5) (5, 0) (0, 5) (5, 0); each side of the square equals and the area of the figure is that expression squared or 50. You can also find the area of a square by multiplying its diagonals by each other and dividing by 2. For example: .
The correct answer is D. How do we know that the area is square and not something else ? Below is the the region we get by joining X and Y intercepts which are (0, 5), (0, 5), (5, 0), (5, 0): Attachment:
MSP254019e3df2hii74417g00000g7c2817hhbe0a3b.gif [ 2.86 KiB  Viewed 2772 times ]
Now, diagonals of the rectangle are equal (10 and 10), and also are perpendicular bisectors of each other (as the are on X and Y axises), so it must be a square. Area of a square equals to diagonal^2/2=10^2/2=50. Answer: D. Similar question: cmatclubtestquestionm25101963.htmlgraphsmodulushelp86549.htmlHope it helps.
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Re: M06#5 Absolute value [#permalink]
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25 Jan 2011, 09:51
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Thanks B one more question please whats the difference between x+y + xy = 4 (A) and x+y =5  (B) For B we find the area through diagonal and for A we simply take one side and square it to get the area.
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Re: M06#5 Absolute value [#permalink]
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25 Jan 2011, 10:01
shrive555 wrote: Thanks B
one more question please
whats the difference between x+y + xy = 4 (A) and x+y =5  (B)
For B we find the area through diagonal and for A we simply take one side and square it to get the area. You can find the area of a square in either way: \(area_{square}=side^2=\frac{diagonal^2}{2}\). The difference between the square given by x+y+xy=4 and the square given by x+y =5 is that the first one is "horizontal" square and the second one is the square turned by 45 degrees. x+y+xy=4: Attachment:
MSP86219e41c890f2h195700001928g4634f4e6h4h.gif [ 1.79 KiB  Viewed 2736 times ]
x+y =5: Attachment:
MSP232619e41b4bhdg1dh6e00003fi9762d3fb98db7.gif [ 2.74 KiB  Viewed 2731 times ]
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Re: M06#5 Absolute value [#permalink]
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26 Feb 2011, 16:40
Bunuel, why cant we assume other values for x + y = 5 it could also be 3 + 8...please advise. i may have a concept wrong
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Re: M06#5 Absolute value [#permalink]
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26 Feb 2011, 17:42
ajit257 wrote: Bunuel, why cant we assume other values for x + y = 5
it could also be 3 + 8...please advise. i may have a concept wrong We are not assuming the values for x and y. We are expanding x + y = 5 to get the figure. If x>0 and y>0 we'll have x+y=5; If x>0 and y<0 we'll have xy=5; If x<0 and y>0 we'll have x+y=5; If x<0 and y<0 we'll have xy=5; So we have 4 lines (4 linear equations which will give 4 segments) when drawn these lines give the square shown in my original post. But there is an easier way to get this figure: get X and Y intercepts (which are (0, 5), (0, 5), (5, 0), (5, 0)) and join them. Follow the links in my previous posts for more.
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Re: M06#5 Absolute value [#permalink]
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26 Feb 2011, 17:45
Bunuel...you're the best....kudos to you
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If equation x+y=5 encloses a certain region on the coordinate plane, what is the area of that region?
A) 5 B) 10 C) 25 D) 50 E) 100
I thought the equation somehow resembled that of a circle centered around the origin. After plugging in some value:
e.g x=2 then y=3 or y=3 x=1 y=4 or 4
I figured that the region might be a circle with a radius of 5, but the explanation says that the figure is a square. Why can't this be a circle?



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Re: m06#5 [#permalink]
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22 Apr 2012, 06:31



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Re: m06#5 [#permalink]
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22 Apr 2012, 06:44
Bunuel wrote: BN1989 wrote: If equation x+y=5 encloses a certain region on the coordinate plane, what is the area of that region?
A) 5 B) 10 C) 25 D) 50 E) 100
I thought the equation somehow resembled that of a circle centered around the origin. After plugging in some value:
e.g x=2 then y=3 or y=3 x=1 y=4 or 4
I figured that the region might be a circle with a radius of 5, but the explanation says that the figure is a square. Why can't this be a circle? Merging similar topics. Please ask if anything remains unclear. Yes, why can't it be a circle?



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Re: m06#5 [#permalink]
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22 Apr 2012, 06:52
BN1989 wrote: Bunuel wrote: BN1989 wrote: If equation x+y=5 encloses a certain region on the coordinate plane, what is the area of that region?
A) 5 B) 10 C) 25 D) 50 E) 100
I thought the equation somehow resembled that of a circle centered around the origin. After plugging in some value:
e.g x=2 then y=3 or y=3 x=1 y=4 or 4
I figured that the region might be a circle with a radius of 5, but the explanation says that the figure is a square. Why can't this be a circle? Merging similar topics. Please ask if anything remains unclear. Yes, why can't it be a circle? Well it cannot be a circle because it's a square. The reason why it's a square is given in previous posts (you can also see a diagram there). Next, in an xy plane, the circle with center (a, b) and radius r is the set of all points (x, y) such that: \((xa)^2+(yb)^2=r^2\). There is no resemblance whatsoever between this equation and the equation given in the question. Hope it's clear.
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Re: M06#5 Absolute value [#permalink]
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14 Apr 2014, 22:04
Hi Bunuel, I understood your concept of equations and plotting points. But, i have a small doubt. Why can't the graph in the second question (x+y =5 )be a horizontal square than a square turned by 45 degrees in the first question (x+y+xy=4) My question is there any reason why in the second question we have plotted a graph which is turned by 45 degrees rather than a horizontal square. Help is appreciated. Thanks in advance Bunuel wrote: shrive555 wrote: Thanks B
one more question please
whats the difference between x+y + xy = 4 (A) and x+y =5  (B)
For B we find the area through diagonal and for A we simply take one side and square it to get the area. You can find the area of a square in either way: \(area_{square}=side^2=\frac{diagonal^2}{2}\). The difference between the square given by x+y+xy=4 and the square given by x+y =5 is that the first one is "horizontal" square and the second one is the square turned by 45 degrees. x+y+xy=4: Attachment: MSP86219e41c890f2h195700001928g4634f4e6h4h.gif x+y =5: Attachment: MSP232619e41b4bhdg1dh6e00003fi9762d3fb98db7.gif




Re: M06#5 Absolute value
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