Coord Geo

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Sun Jan 23, 2011 4:03 am

If r and s are positive numbers, what are the coordinates of the
midpoint of line segment MN in the xy-plane?
(1) The coordinates of M are (r; 3 - s).
(2) The coordinates of N are (3 - r; s).

I don't understand how C works. Doesn't the combined statements just tell you that the midpoint has coordinates that are 1.5 and 1.5 (x,y) away from either point M or N.

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Source: Beat The GMAT — Data Sufficiency | Sun Jan 23, 2011 4:03 am

maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sun Jan 23, 2011 4:08 am

mid point with (x1, y1) (x2, y2) is (x1+x2)/2, (y1+y2)/2

here (r, 3-s) and (3-r, s) results in (3/2), (3/2) so C is fine

Charged up again to beat the beast

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Sun Jan 23, 2011 4:15 am

What if it says, there exists a point X where MX is twice NX. So now the ratio is changed from 1:1 to 2:1. Can you still solve this problem with available info.

For this problem, I imaged X in the middle of points M, N and mentally moved M, N, and X around. There appears to be an infinite possibility for X. Can someone explain why this "formuka" work?

[quote="maihuna"]mid point with (x1, y1) (x2, y2) is (x1+x2)/2, (y1+y2)/2

here (r, 3-s) and (3-r, s) results in (3/2), (3/2) so C is fine[/quote]

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sun Jan 23, 2011 4:19 am

WHat if sun rises in west, what if you eat from your nose... there is no end. Think what if not if, do it the way it is given. People here are not your servant, mind while framing your questions.

yellowho wrote:What if it says, there exists a point X where MX is twice NX. So now the ratio is changed from 1:1 to 2:1. Can you still solve this problem with available info.

For this problem, I imaged X in the middle of points M, N and mentally moved M, N, and X around. There appears to be an infinite possibility for X. Can someone explain why this "formuka" work?

maihuna wrote:mid point with (x1, y1) (x2, y2) is (x1+x2)/2, (y1+y2)/2

here (r, 3-s) and (3-r, s) results in (3/2), (3/2) so C is fine

Charged up again to beat the beast

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Sun Jan 23, 2011 4:39 am

Calm down. I don't have a strong background that's why I'm asking these questions. I don't know the derivation of that formula. I can't careless about the answer. I just want some takeaways from each problem. No where have I demanded anything from anyone. Why do you have to be so pejorative.

[quote="maihuna"]WHat if sun rises in west, what if you eat from your nose... there is no end. Think what if not if, do it the way it is given. People here are not your servant, mind while framing your questions.

[quote="yellowho"]What if it says, there exists a point X where MX is twice NX. So now the ratio is changed from 1:1 to 2:1. Can you still solve this problem with available info.

For this problem, I imaged X in the middle of points M, N and mentally moved M, N, and X around. There appears to be an infinite possibility for X. Can someone explain why this "formuka" work?

[quote="maihuna"]mid point with (x1, y1) (x2, y2) is (x1+x2)/2, (y1+y2)/2

here (r, 3-s) and (3-r, s) results in (3/2), (3/2) so C is fine[/quote][/quote][/quote]

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gmat1011: Master | Next Rank: 500 Posts; Posts: 160; Joined: Mon Apr 05, 2010 4:41 am; Thanked: 7 times

by gmat1011 » Sun Jan 23, 2011 4:49 am

i dont see anything wrong with what yellowwho asked... thats why we have these forum

wtf maihuna? had a bad day or you always like this?

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sun Jan 23, 2011 4:51 am

oK, THATS COOL.

See there are two formulae, general one is called section formulae(internal and external), you can find out the details in any book. The midpoint formulae is simple adding the two end and taking the average, i.e. dividing by two.

see some detail at : https://www.mathisfunforum.com/viewtopic.php?id=3301

maihuna wrote:WHat if sun rises in west, what if you eat from your nose... there is no end. Think what if not if, do it the way it is given. People here are not your servant, mind while framing your questions.

yellowho wrote:What if it says, there exists a point X where MX is twice NX. So now the ratio is changed from 1:1 to 2:1. Can you still solve this problem with available info.

For this problem, I imaged X in the middle of points M, N and mentally moved M, N, and X around. There appears to be an infinite possibility for X. Can someone explain why this "formuka" work?

maihuna wrote:mid point with (x1, y1) (x2, y2) is (x1+x2)/2, (y1+y2)/2

here (r, 3-s) and (3-r, s) results in (3/2), (3/2) so C is fine

[/quote]

Charged up again to beat the beast

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thailandvc: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Fri Jul 24, 2009 5:18 am

by thailandvc » Sun Jan 23, 2011 6:16 am

What's the source of this question? I can't imagine a gmat question testing a somewhat esoteric formula without another way of doing this. Also, r,s>0 suggests that there's another way of doing this problem if you don't know that formula. Anyone know another approach?

Please leave the attitude off the board. Don't respond to the question if you feel its beneath you. Yellow just started studying. Maihuna you have been studying for ~3 years.

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sun Jan 23, 2011 6:56 am

gmat1011 wrote:i dont see anything wrong with what yellowwho asked... thats why we have these forum

wtf maihuna? had a bad day or you always like this?

I m always like this, do whatever u can

Charged up again to beat the beast

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maihuna: Legendary Member; Posts: 1578; Joined: Sun Dec 28, 2008 1:49 amFollowed by: 9 members; Thanked: 82 times; GMAT Score:720

by maihuna » Sun Jan 23, 2011 6:59 am

thailandvc wrote:
Please leave the attitude off the board. Don't respond to the question if you feel its beneath you. Yellow just started studying. Maihuna you have been studying for ~3 years.

i understood his point, its better if u dont rub ur nose here to stretch it further. Probably those who r=will read the post in perspective will understand mine as well. studying for n num of yr is not the point of contention.

Charged up again to beat the beast

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

by Stuart@KaplanGMAT » Sun Jan 23, 2011 7:12 am

thailandvc wrote:What's the source of this question? I can't imagine a gmat question testing a somewhat esoteric formula without another way of doing this. Also, r,s>0 suggests that there's another way of doing this problem if you don't know that formula. Anyone know another approach?

For almost every DS question, there are two general approaches you can take: use math concepts or pick numbers.

So, while you can derive the formula with a bit of common sense, you can also answer the question via picking numbers.

We can quickly eliminate (A), (B) and (D), since each statement provides information about only one of the two endpoints. Accordingly, let's jump right into combination.

(1) The coordinates of M are (r; 3 - s).
(2) The coordinates of N are (3 - r; s).

Based on the question stem r and s are both positive, so let's pick a couple sets of numbers.

r=s=3 seems like a good place to start:

M = (3, 0); N = (0,3). Plot those points on a graph (you get graph-lined scrap paper on test day) and you'll see that the middle is (1.5, 1.5).

Now let's try some different numbers:

r = 1; s=5 gives us M = (1,-2) and N = (-2,5). Plot those points on a graph and you once again get (1.5, 1.5).

You can keep trying different sets of numbers and you'll always get the same midpoint. At some point you'll probably notice that the coordinates of the midpoint are always the average of the coordinates of the end points, deriving the formula mentioned above.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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yellowho: Master | Next Rank: 500 Posts; Posts: 233; Joined: Wed Aug 22, 2007 3:51 pmFollowed by: 2 members; Location: New York; Thanked: 7 times

by yellowho » Sun Jan 23, 2011 7:26 am

Thanks Stuart. Is there a significance of the the statement: r and s are both positives?

I'm used to doing distance problems the distance way. It's more intuitive to me. Without out knowing whether the Xs and Ys are positive (to find distance) I couldn't determine the distance/length and got stuck. Although both r and s are positives, you also have to know whether its greater than 3 to know.

[quote="Stuart Kovinsky"][quote="thailandvc"]What's the source of this question? I can't imagine a gmat question testing a somewhat esoteric formula without another way of doing this. Also, r,s>0 suggests that there's another way of doing this problem if you don't know that formula. Anyone know another approach?

[/quote]

For almost every DS question, there are two general approaches you can take: use math concepts or pick numbers.

So, while you can derive the formula with a bit of common sense, you can also answer the question via picking numbers.

We can quickly eliminate (A), (B) and (D), since each statement provides information about only one of the two endpoints. Accordingly, let's jump right into combination.

(1) The coordinates of M are (r; 3 - s).
(2) The coordinates of N are (3 - r; s).

Based on the question stem r and s are both positive, so let's pick a couple sets of numbers.

r=s=3 seems like a good place to start:

M = (3, 0); N = (0,3). Plot those points on a graph (you get graph-lined scrap paper on test day) and you'll see that the middle is (1.5, 1.5).

Now let's try some different numbers:

r = 1; s=5 gives us M = (1,-2) and N = (-2,5). Plot those points on a graph and you once again get (1.5, 1.5).

You can keep trying different sets of numbers and you'll always get the same midpoint. At some point you'll probably notice that the coordinates of the midpoint are always the average of the coordinates of the end points, deriving the formula mentioned above.[/quote]

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thailandvc: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Fri Jul 24, 2009 5:18 am

by thailandvc » Sun Jan 23, 2011 8:09 am

Actually you are correct. Time studying doesn't matter at all. You shouldn't demean anyone regardless of how long/little they studied or how high/low his/her scores are. I rather look stupid for 5 minutes than be ignorant for life.

maihuna wrote:
thailandvc wrote:
Please leave the attitude off the board. Don't respond to the question if you feel its beneath you. Yellow just started studying. Maihuna you have been studying for ~3 years.
i understood his point, its better if u dont rub ur nose here to stretch it further. Probably those who r=will read the post in perspective will understand mine as well. studying for n num of yr is not the point of contention.

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tailoc: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed Jun 15, 2011 11:38 am; Thanked: 1 times

by tailoc » Sat Oct 08, 2011 7:54 am

Stuart Kovinsky wrote:
thailandvc wrote:What's the source of this question? I can't imagine a gmat question testing a somewhat esoteric formula without another way of doing this. Also, r,s>0 suggests that there's another way of doing this problem if you don't know that formula. Anyone know another approach?

For almost every DS question, there are two general approaches you can take: use math concepts or pick numbers.

So, while you can derive the formula with a bit of common sense, you can also answer the question via picking numbers.

We can quickly eliminate (A), (B) and (D), since each statement provides information about only one of the two endpoints. Accordingly, let's jump right into combination.

(1) The coordinates of M are (r; 3 - s).
(2) The coordinates of N are (3 - r; s).

Based on the question stem r and s are both positive, so let's pick a couple sets of numbers.

r=s=3 seems like a good place to start:

M = (3, 0); N = (0,3). Plot those points on a graph (you get graph-lined scrap paper on test day) and you'll see that the middle is (1.5, 1.5).

Now let's try some different numbers:

r = 1; s=5 gives us M = (1,-2) and N = (-2,5). Plot those points on a graph and you once again get (1.5, 1.5).

You can keep trying different sets of numbers and you'll always get the same midpoint. At some point you'll probably notice that the coordinates of the midpoint are always the average of the coordinates of the end points, deriving the formula mentioned above.

Hi Stuart, coordinates of the midpoint can not be (1.5,1.5) if r = 1; s=5

I found that coordinates of midpoint in this case is (-0.5,1.5). plz, Correct me if I were wrong.

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Sat Oct 08, 2011 8:24 am

tailoc wrote:
Stuart Kovinsky wrote:
thailandvc wrote:What's the source of this question? I can't imagine a gmat question testing a somewhat esoteric formula without another way of doing this. Also, r,s>0 suggests that there's another way of doing this problem if you don't know that formula. Anyone know another approach?

For almost every DS question, there are two general approaches you can take: use math concepts or pick numbers.

So, while you can derive the formula with a bit of common sense, you can also answer the question via picking numbers.

We can quickly eliminate (A), (B) and (D), since each statement provides information about only one of the two endpoints. Accordingly, let's jump right into combination.

(1) The coordinates of M are (r; 3 - s).
(2) The coordinates of N are (3 - r; s).

Based on the question stem r and s are both positive, so let's pick a couple sets of numbers.

r=s=3 seems like a good place to start:

M = (3, 0); N = (0,3). Plot those points on a graph (you get graph-lined scrap paper on test day) and you'll see that the middle is (1.5, 1.5).

Now let's try some different numbers:

r = 1; s=5 gives us M = (1,-2) and N = (-2,5). Plot those points on a graph and you once again get (1.5, 1.5).

You can keep trying different sets of numbers and you'll always get the same midpoint. At some point you'll probably notice that the coordinates of the midpoint are always the average of the coordinates of the end points, deriving the formula mentioned above.
Hi Stuart, coordinates of the midpoint can not be (1.5,1.5) if r = 1; s=5

I found that coordinates of midpoint in this case is (-0.5,1.5). plz, Correct me if I were wrong.

For r=1 and s5
M(1,-2); N(2,5). Midpoint (3/2,3/2)

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