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In the rectangular coordinate system above, if the

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by BTGmoderatorDC » Sun Oct 14, 2018 4:09 am

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In the rectangular coordinate system above, if the coordinates of point P are (5,y), what is the value of y?

(1) The coordinates of point M are (5,0).
(2) The coordinates of point N are (0,−4).

OA B

Source: Princeton Review
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In the rectangular coordinate system above, if the This topi

by fskilnik@GMATH » Sun Oct 14, 2018 7:12 am
BTGmoderatorDC wrote:Image

In the rectangular coordinate system above, if the coordinates of point P are (5,y), what is the value of y?

(1) The coordinates of point M are (5,0).
(2) The coordinates of point N are (0,−4).
Source: Princeton Review
Trivial problem, but nice to present the GEOMETRIC BIFURCATION (of statement (1)):
$$? = y$$
$$\left( 1 \right)\,\,M\,\,{\rm{and}}\,\,P\,\,{\rm{same}}\,\,{\rm{abscissa}}\,\,\left( { = 5} \right)$$
Image

$$\left( 2 \right)\,\,\,N = \left( {0, - 4} \right)\,\,\, \Rightarrow \,\,\,\,\,? = y = - 4\,\,\,\,\,\,\,\left( {P\,\,{\rm{and}}\,\,N\,\,{\rm{same}}\,\,{\rm{ordinate}}} \right)\,\,$$

Image


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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by Brent@GMATPrepNow » Mon Oct 15, 2018 5:08 am
BTGmoderatorDC wrote:Image

In the rectangular coordinate system above, if the coordinates of point P are (5,y), what is the value of y?

(1) The coordinates of point M are (5,0).
(2) The coordinates of point N are (0,−4).
I think that, if this were an official GMAT question, the correct answer would be E (not B), because we aren't specifically told that the dotted lines are parallel to the x-axis and the y-axis.
If those dotted lines aren't parallel to those axes, the we can't determine the value of y.

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by fskilnik@GMATH » Mon Oct 15, 2018 7:38 am
Brent@GMATPrepNow wrote: I think that, if this were an official GMAT question, the correct answer would be E (not B), because we aren't specifically told that the dotted lines are parallel to the x-axis and the y-axis.
If those dotted lines aren't parallel to those axes, the we can't determine the value of y.
I respectfully disagree:

We are told we are in the rectangular coordinate system, we are told about coordinates of points in this rectangular system.

In short: we may implicitly assume the dotted lines are parallel to the x-axis and the y-axis.

Regards,
Fabio.
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