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In xy plane, line K passes through the points A(6, -7)

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by vinni.k » Sat Jan 12, 2013 4:23 am
In xy plane, line K passes through the points A(6, -7) and B(4, 5). Does line K also pass through point C?

(1). Coordinates of Point C are ( 5, -1)
(2). Point C is equidistant from Point A and Point B.

Answer is A

Please explain this question in detail.

Thanks & Regards
Vinni
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by Brent@GMATPrepNow » Sat Jan 12, 2013 8:04 am
vinni.k 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?

(1). Coordinates of Point C are ( 5, -1)
(2). Point C is equidistant from Point A and Point B.
Target question: Does line K pass through point C?

Given: line K passes through the points A(6, -7) and B(4, 5)
NOTE: Once we know two points on line K, we could find the equation of the line, and we could also accurately draw the line on the x-y coordinate plane.

Statement 1: Coordinates of Point C are ( 5, -1)
From the given information, we could accurately draw the line on the x-y coordinate plane.
This would allow us to definitely determine whether or not K passes through point C.
In other words, the information in statement 1 allows us to answer the target question with certainty, which means statement 1 is SUFFICIENT

Statement 2: Point C is equidistant from Point A and Point B.
In other words, point C is such that, we can draw a circle with point C as the center and points A and B as points on the circle (since all points on a line are equidistant from the center).
If we know that line K passes through points A and B (on the circle), can we determine whether or not line K passes through point C (the center)? No.
It could be the case that points A and B are such that line K passes through point C.
Or it could be the case that points A and B are such that line K does not pass through point C.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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by vinni.k » Sat Jan 12, 2013 10:50 am
Thank you Brent :D
Brent@GMATPrepNow wrote:
Target question: Does line K pass through point C?

Given: line K passes through the points A(6, -7) and B(4, 5)
NOTE: Once we know two points on line K, we could find the equation of the line, and we could also accurately draw the line on the x-y coordinate plane.

Statement 1: Coordinates of Point C are ( 5, -1)
From the given information, we could accurately draw the line on the x-y coordinate plane.
This would allow us to definitely determine whether or not K passes through point C.
In other words, the information in statement 1 allows us to answer the target question with certainty, which means statement 1 is SUFFICIENT

Statement 2: Point C is equidistant from Point A and Point B.
In other words, point C is such that, we can draw a circle with point C as the center and points A and B as points on the circle (since all points on a line are equidistant from the center).
If we know that line K passes through points A and B (on the circle), can we determine whether or not line K passes through point C (the center)? No.
It could be the case that points A and B are such that line K passes through point C.
Or it could be the case that points A and B are such that line K does not pass through point C.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
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by sonalibhangay » Sun Jan 13, 2013 8:23 am
By the Points Given , ( 6, -7) and (4, 5), we can find the slope = y2-y1 / x2 -x1 = 5- (-7) / 4-6 = -12/2 = -6

With slope, you get equation of line y = -6x+c to find c, substitute the coordinates of one of the points = you get -7 = -36 +c therefore c=29

To check if the point ( 5, -1 ) is on the line, substituting in the equation, we get --> -1 = -6 (5) +29 --> -1 = - 30 + 29 which holds true, statement 1 is sufficient.

Ans can be A or D .

Check statement 2 which says, point C is equidistant from the above 2 points. this is ambiguous, the point can lie anywhere and be equidistant from both, not necessary that it has to be in centre on same line. B is not sufficient.

ANS A
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by ceilidh.erickson » Tue Jan 15, 2013 10:24 am
Hi Vinni,

If you want a visual representation of why statement (2) is insufficient, look at this diagram:

Image

As you can see, there are points that are equidistant from points A and B that don't lie on the same line. In fact, any point along that red line - the line perpendicular to line AB that intersects it halfway between A and B - will always be equidistant from A and B.
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EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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