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Which of the following points are located within the shaded region of

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Bunuel
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Which of the following points are located within the shaded region of [#permalink] New post   04 Nov 2018, 23:48
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Which of the following points are located within the shaded region of the graph below?

A. (6,1)
B. (-4,0.5)
C. (-4,-0.5)
D. (-4,-4)
E. (-6,1)


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nkin
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Re: Which of the following points are located within the shaded region of [#permalink] New post   05 Nov 2018, 07:33
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As the line passes through (0,0) and (8,2), the equation of the line is x = 4y or x-4y = 0.
Take (8,3) and substitute: we get 8-4*3 = 8 - 12 = -4 < 0 hence above line
Take (8,1) and substitute: we get 8-4*1 = 8 - 4 = 4 > 0 hence below line.

Also, if a point has to be in the shaded region, it has to be in the third quadrant.
ELIMINATE A,B,E. Only options to check are C and D.

D: (-4,-4), substitute: -4 - (4*-4) = -4 +16 = 12 > 0, so below line in third quadrant. Hence eliminate

C: (-4, -0.5), substitute: -4 - (4*-0.5) = -4 + 2 = -2 < 0, so above line in third quadrant. Hence has to be inside the shaded region.

Hence Option C
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Re: Which of the following points are located within the shaded region of [#permalink] New post   12 Nov 2018, 10:04
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Question stem should be: Which of the following points is located...
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Which of the following points are located within the shaded region of [#permalink] New post   12 Nov 2018, 10:27
dimmak wrote:
Question stem should be: Which of the following points is located...



dimmak - IMO the question is correct. "points" is in plural form :grin:
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Re: Which of the following points are located within the shaded region of [#permalink] New post   12 Nov 2018, 10:35
dave13 wrote:
dimmak wrote:
Question stem should be: Which of the following points is located...



dimmak - IMO the question is correct. "points" is in plural form :grin:


But there is just one point that complies. I mean, if you say "are" it would state that there are more than one point that comply with the statement. And because of the essence of the Problem Solving questions, there is just one answer.
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Re: Which of the following points are located within the shaded region of [#permalink] New post   20 Feb 2020, 07:04
nkin wrote:
As the line passes through (0,0) and (8,2), the equation of the line is x = 4y or x-4y = 0.
Take (8,3) and substitute: we get 8-4*3 = 8 - 12 = -4 < 0 hence above line
Take (8,1) and substitute: we get 8-4*1 = 8 - 4 = 4 > 0 hence below line.

Also, if a point has to be in the shaded region, it has to be in the third quadrant.
ELIMINATE A,B,E. Only options to check are C and D.

D: (-4,-4), substitute: -4 - (4*-4) = -4 +16 = 12 > 0, so below line in third quadrant. Hence eliminate

C: (-4, -0.5), substitute: -4 - (4*-0.5) = -4 + 2 = -2 < 0, so above line in third quadrant. Hence has to be inside the shaded region.

Hence Option C


Hi,
Could you please tell me if a line passing through the origin has a constant as in the equation of the line y = mx + c is zero meaning c = 0? If that is true, then i understand why the equation of the line in the question will be x-4y=0. Else, could you explain why ?

Thanks
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Re: Which of the following points are located within the shaded region of [#permalink] New post   21 Feb 2020, 23:51
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This is how I solved it. The shaded region clearly is in the 3rd Quadrant, so options A, B & E are eliminated.

Since the line passes through the origin, the slope of the line can be determined as follows
2-0 / 8-0 = 1/4

Now, for the point to lie in the shaded region, the slope formed by such point with the point (8,2) has to be less than 1/4, which is the slope of our line.
Now, let's test the points in Options C & D
Option C has (-4, -0.5)
So, slope would be 2-(-0.5) / 8-(-4) = 2.5/12, this is less than 1/4.

Option D has (-4, -4)
So, slope would be 2-(-4) / 8-(-4) = 1/2, this is more than 1/4.

Therefore, our answer is Option C.
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Re: Which of the following points are located within the shaded region of [#permalink] New post   13 Mar 2020, 07:56
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slope= y2-y1/x2-x1, using the above diagram we will get our slope as 1/4, thus making the equation of our line as 4y=x or 4y-x=0. If we put put the (-4,-0.5) we get 4*(-0.5)-(-4) = 6, then how are we confirming answer choice C, please explain
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Re: Which of the following points are located within the shaded region of [#permalink] New post   08 Aug 2022, 21:03
ankitprad wrote:
nkin wrote:
As the line passes through (0,0) and (8,2), the equation of the line is x = 4y or x-4y = 0.
Take (8,3) and substitute: we get 8-4*3 = 8 - 12 = -4 < 0 hence above line
Take (8,1) and substitute: we get 8-4*1 = 8 - 4 = 4 > 0 hence below line.

Also, if a point has to be in the shaded region, it has to be in the third quadrant.
ELIMINATE A,B,E. Only options to check are C and D.

D: (-4,-4), substitute: -4 - (4*-4) = -4 +16 = 12 > 0, so below line in third quadrant. Hence eliminate

C: (-4, -0.5), substitute: -4 - (4*-0.5) = -4 + 2 = -2 < 0, so above line in third quadrant. Hence has to be inside the shaded region.

Hence Option C


Hi,
Could you please tell me if a line passing through the origin has a constant as in the equation of the line y = mx + c is zero meaning c = 0? If that is true, then i understand why the equation of the line in the question will be x-4y=0. Else, could you explain why ?

Thanks


Hi, We know that the line given is passing through the origin hence it will not have a y-intercept (c) or the y-intercept = 0 as the definition of y-intercept is the point where a given line passes through the Y-axis. Since the line intersects the origin, it passes through both X and Y axis at (0,0) making 0 your x and y intercept respectively.

I would like to point out that when the line is in the form y=mx + c, point c is used as it is the y-intercept. However when the line is expressed in the form x=my+ b, point b is used to denote the x - intercept which in this case is also 0 as explained above.

Hope this was helpful.
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yash1208
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Re: Which of the following points are located within the shaded region of [#permalink] New post   08 Aug 2022, 21:23
Subhrajyoti wrote:
slope= y2-y1/x2-x1, using the above diagram we will get our slope as 1/4, thus making the equation of our line as 4y=x or 4y-x=0. If we put put the (-4,-0.5) we get 4*(-0.5)-(-4) = 6, then how are we confirming answer choice C, please explain


Hi Subhrajyoti,
I believe you have used the correct method to find the slope and express the line in slope point form. However, we don't need to substitute to find the answer as the question has asked us to identify the point which lies within the shaded region. To verify that option C (-4,-0.5) does lie in the shaded region, we can substitute any one value of either x or y in the equation.

For example,
Equation: 4y=x
- Substituting x= -4 in the equation
We get 4y=-4
and y= -1

This means that the point (-4,-1) lies on the line and hence the point C (-4,-1) will definitely lie within the shaded region

Hope this helps.
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Re: Which of the following points are located within the shaded region of [#permalink]
08 Aug 2022, 21:23
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