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COORDINATE ISSUES!!!!! HELP ASAP

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COORDINATE ISSUES!!!!! HELP ASAP

by AIM TO CRACK GMAT » Tue Oct 15, 2013 6:02 am
Hi everyone!

This is a problem from MGMATs Strategy Guides Geometry

Q- The line represented by the equation y= x is the perpendicular bisector of line segment AB, IF A has the coordinates (-3,3) What are the Coordinates of B????

[spoiler]OA= (3,-3)[/spoiler]
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by theCodeToGMAT » Tue Oct 15, 2013 6:21 am
Please post Answer Choices
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by GMATGuruNY » Tue Oct 15, 2013 6:30 am
Because the GMAT would provide answer choices, we typically can solve this sort of problem by DRAWING:

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by Brent@GMATPrepNow » Tue Oct 15, 2013 6:36 am
AIM TO CRACK GMAT wrote:Hi everyone!

This is a problem from MGMATs Strategy Guides Geometry

Q- The line represented by the equation y= x is the perpendicular bisector of line segment AB, IF A has the coordinates (-3,3) What are the Coordinates of B????

[spoiler]OA= (3,-3)[/spoiler]
Saying that line represented by equation y = x is the perpendicular bisector of line segment AB, is a fancy way of saying that point B is a mirror reflection of point A across the line y = x (in other words, the mirror is the line y = x).

This concept is probably beyond the scope of the GMAT, but if some point (a,b) is reflected across the line y = x, the reflected point is (b,a).
Example: if the point (9,2) is reflected across the line y = x, the reflected point is (2,9)

The question basically tells us that the point (-3, 3) is reflected across the line y = x, so the reflected point (point B) is at [spoiler](3, -3) [/spoiler]

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by AIM TO CRACK GMAT » Tue Oct 15, 2013 6:45 am
Hi... There r no answer choices... this is a problem given in the Problem set at the end of the chapter!!

theCodeToGMAT wrote:Please post Answer Choices
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by mevicks » Tue Oct 15, 2013 7:06 am
AIM TO CRACK GMAT wrote:Hi everyone!

This is a problem from MGMATs Strategy Guides Geometry

Q- The line represented by the equation y= x is the perpendicular bisector of line segment AB, IF A has the coordinates (-3,3) What are the Coordinates of B????

[spoiler]OA= (3,-3)[/spoiler]
You can use the basic Reflection property to find the co-ordinates. Here is the quick drawing:
Image

Since A is equidistant from both the axises, the perpendicular from A would pass through the origin into the IVth quadrant, where the co-ordinates would be reversed to (3, -3)

There is a algebraic approach too, but I think it would not be required on the GMAT!

Regards,
Vivek

Regards,
Vivek
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