Coordinate Geometry

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pm; Thanked: 11 times; Followed by:8 members

Coordinate Geometry

by gmattesttaker2 » Sat Aug 18, 2012 11:44 pm

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Hello,

I was wondering if you can please help with the explanation here. This is from OG 13 P. 318

74) In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

1) The x-coordinate of point R is -1
2) Point R lies on the line y = -3

[spoiler]OA: A[/spoiler]

Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Data Sufficiency | Sat Aug 18, 2012 11:44 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Sun Aug 19, 2012 3:09 am

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gmattesttaker2 wrote:Hello,

I was wondering if you can please help with the explanation here. This is from OG 13 P. 318

74) In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

1) The x-coordinate of point R is -1
2) Point R lies on the line y = -3

[spoiler]OA: A[/spoiler]
Thanks a lot.

Best Regards,
Sri

we need to use a distance formula here for point R (x,y): (x-(-3))^2+(y-(-3))^2=(x-1)^2+(y-(-3))^2 or (x+3)^2+(y+3)^2=(x-1)^2+(y+3)^2 or as evident from the left-hand side and right-hand side we have the same (y+3)^2, therefore, (x+3)^2=(x-1)^2 <-> 8x=-8 and x=-1
Now, if we encounter in any statement x=-1 we should get sufficient information about our point R with coordinates (x,y) as y is not considered in our distance relationship at all.
st(1) x=-1 ==> Sufficient
st(2) y=-3 but we don't know about x-coordinate, Not Sufficient

answer a

Success doesn't come overnight!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Sun Aug 19, 2012 9:04 pm

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gmattesttaker2 wrote:Hello,

I was wondering if you can please help with the explanation here. This is from OG 13 P. 318

74) In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

1) The x-coordinate of point R is -1
2) Point R lies on the line y = -3

[spoiler]OA: A[/spoiler]

Hi!

This question should take about 15 seconds if you actually draw out the x-y plane. There are no bonus points on the GMAT for super-complicated math, so avoid it whenever possible!

If you plot the 2 points, you can see that, since they have the same y-coordinate (-3), one point that's halfway between them is (-1, -3) (the difference in x-coordinates is 4, so if you travel 2 units from either point you'll end up in the middle).

Further, if you draw a vertical line through x=-1, you can see that every point on that line is equidistant from the two points given.

Accordingly, if we know that point R has an x-coordinate of -1, the answer will be YES; if point R has any other x-coordinate, the answer will be NO.

1) gives us the x-coordinate... sufficient!
2) doesn't give us the x-coordinate... insufficient!

(1) is suff, (2) isn't... choose A!

Moral of the story: on geometry word problems, always draw out what you know.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pm; Thanked: 158 times; Followed by:21 members

by pemdas » Mon Aug 20, 2012 2:13 pm

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Stuart Kovinsky wrote:There are no bonus points on the GMAT for super-complicated math, so avoid it whenever possible!

we got lucky that two points of the line segment were given with the same y-coordinate, i.e. parallel to x-abscess. What if we have different points?

Success doesn't come overnight!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Mon Aug 20, 2012 8:56 pm

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pemdas wrote:
Stuart Kovinsky wrote:There are no bonus points on the GMAT for super-complicated math, so avoid it whenever possible!
we got lucky that two points of the line segment were given with the same y-coordinate, i.e. parallel to x-abscess. What if we have different points?

We didn't get lucky - the question was designed to reward people who saw the quick solution.

Most GMAT math questions are designed with 4 levels of reward:

1) negative reward, for people who spend time on it and get it wrong;
2) 0 reward, for people who recognize that they don't know how to solve and get it wrong, but don't waste time on the question;
3) positive reward, for people who take traditional approaches to questions - they get it right, but they spend a lot of time doing so; and
4) super positive reward, for people who find the most efficient solution to the problem - they get it right in a lot less time, leaving more time for other questions.

Never forget - while the GMAT tests math, it's not a math test; the primary skills tested on the GMAT are problem analysis and strategic thinking.

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by Scott@TargetTestPrep » Sun Nov 04, 2018 5:08 pm

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gmattesttaker2 wrote:Hello,

I was wondering if you can please help with the explanation here. This is from OG 13 P. 318

74) In the xy-coordinate plane, is point R equidistant from points (-3,-3) and (1,-3)?

1) The x-coordinate of point R is -1
2) Point R lies on the line y = -3

We need to determine whether point R is equidistant from points (-3,-3) and (1,-3). We know that if point R is on the perpendicular bisector of the line segment with (-3,-3) and (1,-3) as the endpoints, then R is equidistant from (-3,-3) and (1,-3). Since the midpoint of the line segment with endpoints (-3,-3) and (1,-3) is (-1, -3) and the line segment is horizontal, the perpendicular bisector is a vertical line passing through (-1, -3). That is, the perpendicular bisector has equation x = -1. Thus, if point R has an x-coordinate of -1, then point R will be equidistant from (-3,-3) and (1,-3) .

Statement One Alone:

The x-coordinate of point R is -1.

Since the x-coordinate of point R is -1, R is on the line with equation x = -1. That is, R is on the perpendicular bisector of the line segment with endpoints (-3,-3) and (1,-3), so R is equidistant from (-3,-3) and (1,-3). Statement one alone is sufficient to answer the question.

Statement Two Alone:

Point R lies on the line y = -3.

Statement two is not sufficient to answer the question. For example, if R = (-1, -3), then it's equidistant from (-3,-3) and (1,-3). However, if R = (0, -3), then it's not equidistant from (-3,-3) and (1,-3).

Answer: A

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