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

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Re: In the coordinate graph above, if the line passes through the origin, [#permalink]
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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)

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.

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Re: In the coordinate graph above, if the line passes through the origin, [#permalink]
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]
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)

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,

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

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Re: In the coordinate graph above, if the line passes through the origin, [#permalink]
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)

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]
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)

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]
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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]
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Re: In the coordinate graph above, if the line passes through the origin, [#permalink]
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