GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Dec 2019, 07:06

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The coordinates of points A and C are (0, -3) and (3, 3)

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

18 Feb 2012, 18:31
4
34
00:00

Difficulty:

55% (hard)

Question Stats:

68% (02:13) correct 32% (02:24) wrong based on 905 sessions

### HideShow timer Statistics

The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
MBA Section Director
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 7328
City: Pune
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

03 Sep 2013, 22:20
16
8
Refer the first case (i.e. Formula for INTERNAL DIVISION)

In our case $$\frac{m}{n} = \frac{2}{1}$$ AND (x1 y1) = (0,-3) (x2 y2) = (3, 3)

X Coordinate = $$\frac{2(3)+0}{(1+2)}$$ ----------> $$\frac{6}{3}$$ ---------> 2

y Coordinate = $$\frac{2(3)+(-3)}{(1+2)}$$ ----------> $$\frac{3}{3}$$ ---------> 1

Hence B (x y) = 2, 1

Attachments

Untitled.png [ 53.89 KiB | Viewed 52881 times ]

_________________
2020 MBA Applicants: Introduce Yourself Here!

MBA Video Series - Video answers to specific components and questions about MBA applications.

2020 MBA Deadlines, Essay Questions and Analysis of all top MBA programs
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 59709
The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

18 Feb 2012, 18:47
8
3
enigma123 wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

Even though it's possible to set an algebraic equation to get the answer, it would be much easier to draw the line segment AC and you will literally see the answer:
Attachment:

The coordinates.PNG [ 14.83 KiB | Viewed 53700 times ]
Since AB is twice the length of BC then the only acceptable choices is B (2, 1). Two points (1, -5) and (5, 5) does not lie on AC at all, (1.-1) is closer to A than to C and (1.5, 0) divides AC in half.

_________________
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

18 Feb 2012, 19:01
Thanks Bunuel - I didn't get it sorry. How did you arrive at 2 as the co-ordinate for B? Sorry again. Also, I was trying to solve this by using the distance formula for AC.
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 59709
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

18 Feb 2012, 19:05
enigma123 wrote:
Thanks Bunuel - I didn't get it sorry. How did you arrive at 2 as the co-ordinate for B? Sorry again. Also, I was trying to solve this by using the distance formula for AC.

I just put all five points on a plane and saw that the only acceptable answer is C (2, 1). Look at other 4 points (blue) on the diagram and read my explanation: neither of them can divided AC into ratio 2:1.
_________________
Intern
Joined: 28 Mar 2011
Posts: 7
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

03 Sep 2013, 11:24
Bunuel wrote:
enigma123 wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

Even though it's possible to set an algebraic equation to get the answer, it would be much easier to draw the line segment AC and you will literally see the answer:
Attachment:
The coordinates.PNG
Since AB is twice the length of BC then the only acceptable choices is C (2, 1). Two points (1, -5) and (5, 5) does not lie on AC at all, (1.-1) is closer to A than to C and (1.5 0) divides AC in half.

question says AB=2AC and B is the in between point of AC. it can be inferred from that B is the middle point of AC. So, all it need to find out the midpoint of AC.

M1= 3-0/2 = 1.5
M2= 3-3/2 = 0

So, B (1.5, 0)

If I am wrong please correct me.
Math Expert
Joined: 02 Sep 2009
Posts: 59709
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

03 Sep 2013, 11:30
zachowdhury wrote:
Bunuel wrote:
enigma123 wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

Even though it's possible to set an algebraic equation to get the answer, it would be much easier to draw the line segment AC and you will literally see the answer:
Attachment:
The coordinates.PNG
Since AB is twice the length of BC then the only acceptable choices is C (2, 1). Two points (1, -5) and (5, 5) does not lie on AC at all, (1.-1) is closer to A than to C and (1.5 0) divides AC in half.

question says AB=2AC and B is the in between point of AC. it can be inferred from that B is the middle point of AC. So, all it need to find out the midpoint of AC.

M1= 3-0/2 = 1.5
M2= 3-3/2 = 0

So, B (1.5, 0)

If I am wrong please correct me.

The questions says that AB = 2BC, not that AB=2AC.
_________________
Intern
Joined: 18 Aug 2013
Posts: 13
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

03 Sep 2013, 17:51
1
How would you find the coordinates algebraically?

I've done problems where AB=3BC, so you can easily find the average of two points, then again average the midpoint and C to find the answer, but that is not possible for a problem like this where the ratio of distance is 2:1.

Thanks
Director
Joined: 25 Apr 2012
Posts: 651
Location: India
GPA: 3.21
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

03 Sep 2013, 22:14
enigma123 wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

For the Graph,please look at Bunuel's post.

We can find distance between points A & C using the distance formula : \sqrt{(x2-x1)^2 +(y2-y1)^2}

We get \sqrt{(3-0)^2+(3-(-3))^2} ------> \sqrt{45}

Now at point B ---> AB= 2 BC ------> AB+BC =\sqrt{45} or 3BC =\sqrt{45} ----> BC =\sqrt{5}
So distance from C to B will be \sqrt{5}

Now from answer choice, we can see only option C gives as \sqrt{5} as the distance between Point B and C

Bunuel's reply is more crisp and time saving.
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Math Expert
Joined: 02 Sep 2009
Posts: 59709
Re: The coordinates of points A and C are (0, -3) and (3, 3),  [#permalink]

### Show Tags

21 Oct 2013, 10:10
Bunuel wrote:
AccipiterQ wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A (1, -$$\sqrt{5}$$)
B (1, -1)
C (2, 1)
D (1.5, 0)
E ($$\sqrt{5}$$,$$\sqrt{5}$$)

could not get this one for the life of me; I calculated what the length of AC was, but after that didn't know how to solve

Spoiler: :: OE
Point B is on line AC, two-thirds of the way between Point A and Point C. To find the coordinates of point B, it is helpful to imagine that you are a point traveling along line AC.

When you travel all the way from point A to point C, your x-coordinate changes 3 units (from x = 0 to x = 3). Two-thirds of the way there, at point B, your x-coordinate will have changed 2/3 of this amount, i.e. 2 units. The x-coordinate of B is therefore x = 0 + 2 = 2.
When you travel all the way from point A to point C, your y-coordinate changes 6 units (from y = -3 to y = 3). Two-thirds of the way there, at point B, your y-coordinate will have changed 2/3 of this amount, i.e. 4 units. The y-coordinate of B is therefore y = -3 + 4 = 1.

Thus, the coordinates of point B are (2,1).

Merging similar topics. Please refer to the solutions above.

Similar question to practice:
in-the-rectangular-coordinate-system-above-the-line-y-x-144774.html
in-the-xy-coordinate-plane-is-point-r-equidistant-from-143502.html
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
in-the-rectangular-coordinate-system-the-line-y-x-is-the-88473.html
in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html
the-line-represented-by-the-equation-y-4-2x-is-the-127770.html
points-m-5-2-and-n-5-8-lie-on-the-xy-127803.html
line-segments-ab-and-cd-are-of-equal-length-and-perpendicula-159799.html

Hope it helps.
_________________
Manager
Joined: 21 Oct 2013
Posts: 177
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

24 Jan 2014, 04:47
1
y = mx + n

n = -3 (from point A)
3 = 3m -3 (from point C)
m=2
Equation of line AC: y = 2x - 3

Now put in the given answers. None works except from C and D. Both points lie on the line. From the question we know that AB = 2BC. So lets calculate the middle of the line AC. (Xa+Xb)/2 = 0+3 / 2 = 1.5 and (Ya+Yb)/2 = -3+3 / 2 = 0

SO we have M = (1.5;0) which is answer D. Hence answer C is correct.
Senior Manager
Joined: 07 Aug 2011
Posts: 499
GMAT 1: 630 Q49 V27
The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

22 Mar 2015, 09:52
enigma123 wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

I think this question can be solved without pen and paper .
if B were at mid of A and C the coordinates of B were (1.5,0) but we are told that B is closer to C so definitely X coordinate will be more than 1.5 , only 1 point in list of options makes sense . option D . Ignore Option E as it lies outside the line segment AC as we are told that 'point B lies on line AC between points A and C'

noticed that there are edits to the option E from (5,5) to ( $$\sqrt{5},\sqrt{5}$$), so possible options are C and E .
Slope of line AC=$$\frac{2}{1}$$ slope of AB should be same as slope of AC
slope of AC = $$(\sqrt{5}+3)/(\sqrt{5} - 0)$$ this cannot be equal to 2.
Senior Manager
Joined: 08 Dec 2015
Posts: 285
GMAT 1: 600 Q44 V27
The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

11 Jun 2016, 10:12
1
Want a really long way to solve this? No fancy formulas no estimation on paper.

We have from the known coordinates that the big triangle has sides 3, 6, 3BC.

So, $$3^2+6^2=3BC^2$$

We get that $$bc=\sqrt{5}$$

Note that now we have a smaller triangle

Then, using the proportions given, so AB=2BC, we can determine that the h of the small triangle is 2.
We can also calculate the other side since we know the hypotenuse ($$\sqrt{5}$$)

So: $$\sqrt{5}=2^2+x^2$$ X=1

Then we can use the same concept of proportions AB=2BC to determine that$$\sqrt{5}$$ segment corresponds
to 1\3rd of the big triangle. So, the distance from origin on X-axis to the side (base) of the small triangle is 2. And that means that C (2,y). We got our X.

Now get the linear equation of the hypotenuse of the big triangle. Using the given points A and B, we get that slope=6/3 or 2 and y-intercept is -3

So y=2x-3

Now plug-in the X=2 to get that Y=1

Answer C. Logical deduction + Pythagoras Theorem only.
Attachments

triangle 1.jpg [ 21.16 KiB | Viewed 45471 times ]

Manager
Joined: 29 May 2016
Posts: 92
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

13 Jul 2016, 23:01
First of all point is closer to C. to get exact coordinates
how much distance from y axis will give us X coordinate and distance from x axis will give us Y coordinate
difference of Y coordinates of two points 3-0= 3
now this distance will be divided in such a way that it will give us AB :BC 2:1 ratio. X coordinate will be two.
similarly Y ccordinate will be 3-(-3) = 6
2:1 is 4 is to 2; from -3 it will 4 points that is 1
(2,1)
Current Student
Joined: 23 Jul 2015
Posts: 139
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

11 Jan 2017, 12:09
Let co-ordinate of B = $$(x_1, y_1)$$
Therefore, $$x_1 - 0 = 2(3 - x_1)$$ ==>$$3(x_1) = 6$$ => $$x_1 = 2$$
$$y_1 - (-3) = 2 (3 - y_1)$$==> $$3(y_1) = 6 -3$$ ==> $$y_1 = 1$$
Ans.: C
Director
Joined: 12 Nov 2016
Posts: 694
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

14 Jun 2017, 22:18
enigma123 wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

For coordinate geometry questions its important to have dry erase grid broad- these questions can be more difficult than they need to be and you can end up doing more math then you really need to without a coordinate plane. An dry erase board with a coordinate plane on it can be purchased here

https://www.amazon.com/Manhattan-GMAT-S ... %2F+Marker

Secondly, the key word in this question is "coordinate." There is no need to find the distance between point a and c and there is no need to draw out similar triangles- with a coordinate plan we could simply draw this on the board- now, if AB=2BC then that simply means point B would 2/3 of the height and thus

C
Intern
Joined: 09 Oct 2016
Posts: 32
The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

16 Sep 2017, 07:48
enigma123 wrote:
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

A. (1, -5)
B. (1, -1)
C. (2, 1)
D. (1.5, 0)
E. (5, 5)

How this can be solved guys?

The length of AC = √((x1-x2)^2 )+(y1-y2)^2 = √((0-3)^2 )+(-3-3)^2 = √45 = 3√5
From the question AB = 2BC, this means that AB = 2√5 and BC = √5
By applying the length formula In the multiple choices, the correct answer should give us the right lengths of AB and BC.
Choice C does that:
AB = √((x1-x2)^2 )+(y1-y2)^2 = √((0-2)^2 )+(-3-1)^2 = √20 = 2√5
BC = = √((x1-x2)^2 )+(y1-y2)^2 = √((3-2)^2 )+(3-1)^2 = √5
Non-Human User
Joined: 09 Sep 2013
Posts: 13744
Re: The coordinates of points A and C are (0, -3) and (3, 3)  [#permalink]

### Show Tags

01 Oct 2018, 04:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The coordinates of points A and C are (0, -3) and (3, 3)   [#permalink] 01 Oct 2018, 04:37
Display posts from previous: Sort by