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m05 #13

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m05 #13 [#permalink] New post 31 May 2012, 08:10
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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?
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Re: m05 #13 [#permalink] New post 31 May 2012, 08:52
gmatmember85 wrote:
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?

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.
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Re: m05 #13 [#permalink] New post 31 May 2012, 08:58
Expert's post
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.

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Re: m05 #13   [#permalink] 31 May 2012, 08:58
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