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Coordinate Geometry prob

by selango » Thu May 20, 2010 9:37 pm

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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?
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by liferocks » Thu May 20, 2010 9:45 pm
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
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by selango » Thu May 20, 2010 9:51 pm
How do u calculate m1 and m2?
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by liferocks » Thu May 20, 2010 9:55 pm
selango wrote:How do u calculate m1 and m2?
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 2:1
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by rbansal » Mon May 02, 2011 7:45 pm
can someone please explain this question in detail I am still having troubles with it.

Thank you,

RB
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by GMATGuruNY » Mon May 02, 2011 7:57 pm
selango wrote:Image

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?
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.
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by smackmartine » Mon May 02, 2011 9:04 pm
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?
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by sugmomo » Tue May 03, 2011 4:02 am
Hi everyone,

I m not able to see the attached picture.. pls. help..
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by rohu27 » Tue May 03, 2011 8:39 am
GMATGuruNY wrote:
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?
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.
Mitch,
under what instances can we take the figures to be accurate and to the scale and under what instances we cannot?

Thanks,
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by enjoylife1788 » Sat Oct 29, 2011 9:19 pm
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
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... :)
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by factor26 » Sun Oct 30, 2011 4:18 pm
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.
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by anjalimanas » Mon Jul 30, 2012 10:52 pm
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
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by frankodern » Sat Feb 08, 2014 7:43 am
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.
GMATGuruNY wrote:
selango wrote:Image

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?
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.
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by [email protected] » Sun Feb 09, 2014 11:51 am
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.

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by Jeff@TargetTestPrep » Thu Apr 05, 2018 10:26 am

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)
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.

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

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Head of GMAT Instruction
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