coordinate geometry

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siddhans: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Sun Aug 22, 2010 2:55 pm

by siddhans » Sun Nov 20, 2011 10:30 am

In the rectangular coordinate system below, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary lines?

A. x = 0
B. y = 0
C. x = 1
D. x - y = 0
E. x + 2y = 2

Can someone please give a MEANINGFUL DEAILED explanation so I can understand ??? I am not good at coordinate geometry ??

PLEASE HELP

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Source: Beat The GMAT — Problem Solving | Sun Nov 20, 2011 10:30 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Sun Nov 20, 2011 10:43 am

Method 1

Refer to the diagram above.

The shaded region is bounded by the X axis, Y axis, the red and the blue lines.

Equation for X axis --> y = 0
Equation for Y axis --> x = 0
Equation for red line --> x = 1

Hence, first 3 options are discarded.

Now the blue line is a line with negative slope. Between option D and E, E has a negative slope.

Hence, D is not the equation of any boundary line.

Method 2
Have a look at the options. Option D is equivalent to x = y, which is the equation of a line passing through the origin with a positive slope (= 1). Just by looking at the diagram we can say that x = y is not one of the boundary lines.

The correct answer is D.

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vishal.pathak: Master | Next Rank: 500 Posts; Posts: 176; Joined: Thu Sep 22, 2011 5:32 am; Thanked: 5 times

by vishal.pathak » Sun Nov 20, 2011 10:46 am

siddhans wrote:In the rectangular coordinate system below, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary lines?

A. x = 0
B. y = 0
C. x = 1
D. x - y = 0
E. x + 2y = 2

Can someone please give a MEANINGFUL DEAILED explanation so I can understand ??? I am not good at coordinate geometry ??

PLEASE HELP

From the figure it is cleat that x axis and y axis are the sides of this quad
eqn of x axis is y=0 and that of y axis is x=0
We can also see a line parallel to x axis, and passing through (1,0). Since it is parallel to y axis so its eqn is similar to y axis and takes into account , the fact that it passes through (1,0). Eqn of this line is x = 1
Now pick any point on the last line. Lets pick (2,0). Put this value in the final 2 eqns and you will find that x + 2y = 2 is satisfied by this point.
So the only eqn which does not represent any line is x-y = 0

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siddhans: Senior | Next Rank: 100 Posts; Posts: 65; Joined: Sun Aug 22, 2010 2:55 pm

by siddhans » Sun Nov 20, 2011 12:06 pm

vishal.pathak wrote:
siddhans wrote:In the rectangular coordinate system below, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary lines?

A. x = 0
B. y = 0
C. x = 1
D. x - y = 0
E. x + 2y = 2

Can someone please give a MEANINGFUL DEAILED explanation so I can understand ??? I am not good at coordinate geometry ??

PLEASE HELP
From the figure it is cleat that x axis and y axis are the sides of this quad
eqn of x axis is y=0 and that of y axis is x=0
We can also see a line parallel to x axis, and passing through (1,0). Since it is parallel to y axis so its eqn is similar to y axis and takes into account , the fact that it passes through (1,0). Eqn of this line is x = 1
Now pick any point on the last line. Lets pick (2,0). Put this value in the final 2 eqns and you will find that x + 2y = 2 is satisfied by this point.
So the only eqn which does not represent any line is x-y = 0

Hi,

If we put (2,0) in the equation x-y=0 we get 2-y=0 thus y=2...so how do we determine that the line x-y is not satisfied by this equation. Is it because no line passes at point y=2 when x=2?

Also, if we put (2,0) in x + 2y = 2

we get 2 + 0 = 2 Thus equation x + 2y = 2 is satisfied . Lets say we put another point (0,1) from that line in the equation then we get 0 + 2(1) = 2 and thus the equation is satisfied again.

Besides 2,0 and 0,1 can we put any other point from any of the other lines ? say x=1 from the line which is parallel to y axis ? Will that work?

Please reply to my bolded questions. Awaiting reply. Thanks in advance

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Nov 22, 2017 12:28 pm

siddhans wrote:In the rectangular coordinate system below, the shaded region is bounded by straight lines. Which of the following is NOT an equation of one of the boundary lines?

A. x = 0
B. y = 0
C. x = 1
D. x - y = 0
E. x + 2y = 2

The vertical line on the left (which is also the y-axis) has the equation of x = 0.

The vertical line on the right has the equation of x = 1.

The horizontal line at the bottom (which is also the x-axis) has the equation of y = 0.

The diagonal line at the top has the equation of y = (-Â½)x + 1. When simplifying answer choice E, we see that we have that same equation:

x + 2y = 2

2y = -x + 2

y = (-Â½)x + 1

Thus, the correct answer is D.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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