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31 May 2012, 09:10
Kudos
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In xy plane, line K passes through the points A(6, -7) and B(4, 5). Does line K also pass through point C?
Coordinates of Point C are ( 5, -1)
Point C is equidistant from Point A and Point B.
I don't quite understand this.. can someone please explain clearly?
Coordinates of Point C are ( 5, -1)
Point C is equidistant from Point A and Point B.
I don't quite understand this.. can someone please explain clearly?
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31 May 2012, 09:52
Kudos
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gmatmember85
Using the given information, we know an equation for the line K is y+7=((-7-5)/(6-4))(x-6)=-6*(x-6). Given an equation for the line, the coordinates of any point on the xy-plane are sufficient to determine whether it is on the line. Hence, statement 1 is sufficient. Statement 2 is not sufficient because any point on the line perpendicular to K passing through the midpoint of AB is equidistant from A and B. Clearly the midpoint of AB lies on AB but the other points do not. The answer is A.
31 May 2012, 09:58
Kudos
Bookmarks
In xy plane, line K passes through the points A(6, -7) and B(4, 5). Does line K also pass through point C?
Notice that since we have two distinct points of line K, then we can find its equation.
(1) Coordinates of Point C are (5, -1) --> we know the equation of line K, hence we can find whether it passes through some particular point. Sufficient.
(2) Point C is equidistant from point A and point B --> point C may be the midpoint of the line segment AB, so on line K. But point C can also be anywhere on the line which is perpendicular to line K and passes through that midpoint. Not sufficient.
Answer: A.
Notice that since we have two distinct points of line K, then we can find its equation.
(1) Coordinates of Point C are (5, -1) --> we know the equation of line K, hence we can find whether it passes through some particular point. Sufficient.
(2) Point C is equidistant from point A and point B --> point C may be the midpoint of the line segment AB, so on line K. But point C can also be anywhere on the line which is perpendicular to line K and passes through that midpoint. Not sufficient.
Answer: A.
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
Where to now? Try our up-to-date Free Adaptive GMAT Club Tests
for the latest questions.
Still interested? Check out the "Best Topics" block above for better discussion and related questions.
Thank you for understanding, and happy exploring!
