Source:OG 12 Prob:39
In the figure above, the point on segment PQ that is twice as far from P as from Q is
A) (3,1)
B) (2,1)
C) (2,-1)
D) (1.5,0.5)
E) (1,0)
Can anyone solve this in detail?
Coordinate Geometry prob
This topic has expert replies
-
- Legendary Member
- Posts: 576
- Joined: Sat Mar 13, 2010 8:31 pm
- Thanked: 97 times
- Followed by:1 members
if any point O(x,y) divides distance between two point A(x1,y1) and B(x2,y2) in the ratio m1:m2
co ordinates of the point O is
x=(m1x2+m2x1)/(m1+m2) and y=(m1y2+m2y1)/(m1+m2)
here A(x1,y1)=P(0,-1) ..B(x2,y2)=Q(3,2) and m1:m2=2:1
so the coordinate of the point on segment PQ that is twice as far from P as from Q is
x=(2*3+0*1)/3=2 y=(2*2+(-1)*1)/3 =1
or(2,1)
Ans option B
co ordinates of the point O is
x=(m1x2+m2x1)/(m1+m2) and y=(m1y2+m2y1)/(m1+m2)
here A(x1,y1)=P(0,-1) ..B(x2,y2)=Q(3,2) and m1:m2=2:1
so the coordinate of the point on segment PQ that is twice as far from P as from Q is
x=(2*3+0*1)/3=2 y=(2*2+(-1)*1)/3 =1
or(2,1)
Ans option B
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
-
- Legendary Member
- Posts: 576
- Joined: Sat Mar 13, 2010 8:31 pm
- Thanked: 97 times
- Followed by:1 members
It has been given that the point on segment PQ that is twice as far from P as from Q..read the bold section carefully.It gives the ratio as 2:1selango wrote:How do u calculate m1 and m2?
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Don't calculate; use the answer choices.
The x coordinate of P is 0.
The x coordinate of Q is 3.
The midpoint between P and Q has an x coordinate of (0+3)/2 = 1.5
Thus, the x coordinate of a point closer to Q must be between 1.5 and 3.
Eliminate A, D, and E.
In answer choices B and C, x=2.
Since at x=2 line segment PQ is above the x axis, the y coordinate must be positive.
Eliminate C.
The correct answer is B.
Last edited by GMATGuruNY on Sat Sep 10, 2011 2:33 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- smackmartine
- Legendary Member
- Posts: 516
- Joined: Fri Jul 31, 2009 3:22 pm
- Thanked: 112 times
- Followed by:13 members
selango wrote:Source:OG 12 Prob:39
In the figure above, the point on segment PQ that is twice as far from P as from Q is
A) (3,1)
B) (2,1)
C) (2,-1)
D) (1.5,0.5)
E) (1,0)
Can anyone solve this in detail?
- Attachments
-
-
- Legendary Member
- Posts: 586
- Joined: Tue Jan 19, 2010 4:38 am
- Thanked: 31 times
- Followed by:5 members
- GMAT Score:730
Mitch,GMATGuruNY wrote:Don't calculate; use the answer choices.selango wrote:Source:OG 12 Prob:39
In the figure above, the point on segment PQ that is twice as far from P as from Q is
A) (3,1)
B) (2,1)
C) (2,-1)
D) (1.5,0.5)
E) (1,0)
Can anyone solve this in detail?
The x coordinate of P is 0.
The x coordinate of Q is 3.
The midpoint between P and Q has an x coordinate of (0+3)/2 = 1.5
Thus, the x coordinate of a point closer to Q must be between 1.5 and 3.
Eliminate A, D, and E.
In answer choices B and C, x=2.
Since at x=2 line segment PQ is above the x axis, the y coordinate must be positive.
Eliminate C.
The correct answer is B.
under what instances can we take the figures to be accurate and to the scale and under what instances we cannot?
Thanks,
-
- Senior | Next Rank: 100 Posts
- Posts: 38
- Joined: Sat Aug 15, 2009 10:31 pm
- Location: India
I guess this is nothing but the weighted average formula. Isnt it?? Can we interpret it that way?? but after seeing this solution of yours, I remembered that I had learnt something like this in school. Its all school quant, but we just dont remember it after so long...liferocks wrote:if any point O(x,y) divides distance between two point A(x1,y1) and B(x2,y2) in the ratio m1:m2
co ordinates of the point O is
x=(m1x2+m2x1)/(m1+m2) and y=(m1y2+m2y1)/(m1+m2)
here A(x1,y1)=P(0,-1) ..B(x2,y2)=Q(3,2) and m1:m2=2:1
so the coordinate of the point on segment PQ that is twice as far from P as from Q is
x=(2*3+0*1)/3=2 y=(2*2+(-1)*1)/3 =1
or(2,1)
Ans option B
look at the answer choices given ...
a - 3,1 --- does not appear to be on the line ... eliminate from answer choices
b - 2,1 --- appears to be on the line --- lets come back to this
c - 2,-1 --- not on line pq -- eliminate from answer choices
d - 1.5,.5 --- possibly on the line --- lets revisit later
e - 1,0 --- likewise, lets revisit later
from just looking at the answer choices and the graph provided we eliminated 2 of 5 answer choices ... now lets get back to the problem!
we can make right triangles given the points provided in the answer choices where the height is represented by drawing a vertical line stopping at the y point in the answer choice and going horizontal to the x point.
B)2,1 --- using the Pythagorean theorm ... we find the hyp or the diagional of the line given for distances... the smaller triangle is 2rad2 and the larger is 3rad2 ... 3rad2-2rad2 is 1 rad 2 --which is the distance from the point on the graph to point q
the result is a 2;1 ratio where p, (2,1) is twice the distance of (2,1), q ... thus b is the answer.
a - 3,1 --- does not appear to be on the line ... eliminate from answer choices
b - 2,1 --- appears to be on the line --- lets come back to this
c - 2,-1 --- not on line pq -- eliminate from answer choices
d - 1.5,.5 --- possibly on the line --- lets revisit later
e - 1,0 --- likewise, lets revisit later
from just looking at the answer choices and the graph provided we eliminated 2 of 5 answer choices ... now lets get back to the problem!
we can make right triangles given the points provided in the answer choices where the height is represented by drawing a vertical line stopping at the y point in the answer choice and going horizontal to the x point.
B)2,1 --- using the Pythagorean theorm ... we find the hyp or the diagional of the line given for distances... the smaller triangle is 2rad2 and the larger is 3rad2 ... 3rad2-2rad2 is 1 rad 2 --which is the distance from the point on the graph to point q
the result is a 2;1 ratio where p, (2,1) is twice the distance of (2,1), q ... thus b is the answer.
-
- Junior | Next Rank: 30 Posts
- Posts: 18
- Joined: Fri Apr 27, 2012 1:49 am
the post is a bit too late :-
since the point has to be twice as far from P as from Q means the point divides the line in the ratio 2:1 so te x co-ordinate = (0 + 3)/3 = 1, y co-ordinate = (2 - (-1))/3 = 1
from P(0,-1) --> first point (0+1, -1+1) = (1,0) and second point (1+1, 0+1) = (2,1) are points that divide the segment PQ in three equal parts
since we need a point which is twice away from P as from Q, (2,1) is the answer
since the point has to be twice as far from P as from Q means the point divides the line in the ratio 2:1 so te x co-ordinate = (0 + 3)/3 = 1, y co-ordinate = (2 - (-1))/3 = 1
from P(0,-1) --> first point (0+1, -1+1) = (1,0) and second point (1+1, 0+1) = (2,1) are points that divide the segment PQ in three equal parts
since we need a point which is twice away from P as from Q, (2,1) is the answer
-
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Tue Jan 14, 2014 3:34 pm
Mitch, can you please explain or simplify this statement "the point that is twice as far from P as from Q?"
From my understanding this means that point is 2x the distance from P and 2x the distance from Q or simply in the middle of the two. Am I reading this correctly?
Greatly appreciate your assistance.
From my understanding this means that point is 2x the distance from P and 2x the distance from Q or simply in the middle of the two. Am I reading this correctly?
Greatly appreciate your assistance.
GMATGuruNY wrote:Don't calculate; use the answer choices.
The x coordinate of P is 0.
The x coordinate of Q is 3.
The midpoint between P and Q has an x coordinate of (0+3)/2 = 1.5
Thus, the x coordinate of a point closer to Q must be between 1.5 and 3.
Eliminate A, D, and E.
In answer choices B and C, x=2.
Since at x=2 line segment PQ is above the x axis, the y coordinate must be positive.
Eliminate C.
The correct answer is B.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi frankodern,
The point that is "twice as far from P as from Q" is NOT the same distance from both. The point would be closer to Q; whatever THAT distance is, the distance to point P is TWICE that distance.
GMAT assassins aren't born, they're made,
Rich
The point that is "twice as far from P as from Q" is NOT the same distance from both. The point would be closer to Q; whatever THAT distance is, the distance to point P is TWICE that distance.
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Looking at the diagram, we need to determine which answer choice gives us a point on the graph that is twice as far from P as from Q. This means that it is closer to Q than to P.
In the figure above, the point on segment PQ that is twice as far from P as from Q is
A) (3,1)
B) (2,1)
C) (2,-1)
D) (1.5,0.5)
E) (1,0)
We can see that point Q is at (3,2) and point P is at (0,-1). Let's start with answer choice A.
A) (3,1)
Looking at the graph we see that (3,1) is not even on line segment PQ. Answer choice A is not correct.
B) (2,1)
Looking at the graph we see that (2,1) is on line segment PQ and it is closer to Q than it is to P. We could use the distance formula to determine the actual distances, but let's wait to see if this is necessary. Let's test the other answer choices to be certain that answer choice B is correct.
C) (2,-1)
Looking at the graph we see that (2,-1) is not even on line segment PQ. Answer choice C is not correct.
D) (1.5,0.5)
Looking at the graph we see that (1.5,0.5) is on line segment PQ; however, it appears to be about halfway between P and Q. Answer choice D is not correct.
E) (1,0)
Looking at the graph we see that (1,0) is on line segment PQ; however, it is closer to P than to Q. Answer choice E is not correct.
Answer: B
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews