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In the coordinate graph above, if the line passes through the origin,

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Bunuel
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In the coordinate graph above, if the line passes through the origin, [#permalink] New post  17 Jan 2016, 11:45
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In the coordinate graph above, if the line passes through the origin, which of the following could be the coordinates of point P?

A. (1, 1)
B. (−1, 0)
C. (−1, 1)
D. (−2, 0)
E. (−2, −1)

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2016-01-17_2244.png
2016-01-17_2244.png [ 3.22 KiB | Viewed 4457 times ]
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  19 Jan 2016, 09:58
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I feel the answer is E. Slope of (2,1) & (0,0) should be same as P(x,y). Also it lies in third quadrant where both x & y are negative.
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  19 Jan 2016, 10:51
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(2,1) and (0,0)
Slope, m = (y2-y1)/(x2-x1) = 1-0/2-0
= 1/2

Y= mx + c
Substituting X=0 and y = 0,
C=0.
Therefore y=0.5x
Only option E satisfies this equation.
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  19 Jan 2016, 11:10
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Bunuel wrote:

In the coordinate graph above, if the line passes through the origin, which of the following could be the coordinates of point P?

A. (1, 1)
B. (−1, 0)
C. (−1, 1)
D. (−2, 0)
E. (−2, −1)

Show Spoiler
Attachment:
2016-01-17_2244.png



For any line passing through the origin, every point (a,b) has a corresponding point (-a,-b).

We are given that the line passes through the origin, and point (2,1). Therefore the point (-2,-1) must also be on the line.

Answer E
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  24 Apr 2016, 23:59
well the trick that i used to solve this question was point P lies in 3rd quadrant
so both x and y has to be negative which is only option E.

also the right way is to find the approach from the given point and origin we know that the slope is 1/2.. so we can check that out..

i used mixed approach.. first as i assumed E, i then checked the slope,
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In the coordinate graph above, if the line passes through the origin, [#permalink] New post  14 Jul 2016, 07:36
Bunuel wrote:

In the coordinate graph above, if the line passes through the origin, which of the following could be the coordinates of point P?

A. (1, 1)
B. (−1, 0)
C. (−1, 1)
D. (−2, 0)
E. (−2, −1)

Show Spoiler
Attachment:
2016-01-17_2244.png


Two methods to solve this
Visual method :- P lies in third quadrant. In Q III both x and y are always negative
Therefore only E matches out requirement,
Answer is E

Algebric Method :-
slope = y2-y1/x2-x1
at x=0 y = 0 (as per the diagram, because the line is passing through the centre)
therefore
Slope = 2-0/1-0
y/x=2
y=1/2 x + 0
or x=2y

Only E is the solution to this equation

ANSWER IS E
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  26 May 2019, 06:55
Bunuel wrote:

In the coordinate graph above, if the line passes through the origin, which of the following could be the coordinates of point P?

A. (1, 1)
B. (−1, 0)
C. (−1, 1)
D. (−2, 0)
E. (−2, −1)

Show Spoiler
Attachment:
2016-01-17_2244.png


P lies in Quadrant III, so x and y must be negative. The only answer that satisfies this criterion is E
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  26 May 2019, 07:03
Bunuel wrote:

In the coordinate graph above, if the line passes through the origin, which of the following could be the coordinates of point P?

A. (1, 1)
B. (−1, 0)
C. (−1, 1)
D. (−2, 0)
E. (−2, −1)

Show Spoiler
Attachment:
2016-01-17_2244.png



P is in the third quadrant where both the coordinates are -ve. So E
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  07 Sep 2021, 05:24
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The signs of both the coordinates in Quadrant III for the point P are negative.

The only answer option with both coordinates negative are in option e.

(option e)

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Re: In the coordinate graph above, if the line passes through the origin, [#permalink] New post  07 Jun 2023, 23:24
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink]
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