GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Feb 2020, 21:39 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The coordinates of points A and C are (0, -3) and (3, 3), respectively

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), respectively  [#permalink]

### Show Tags

4
39 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:12) correct 33% (02:25) wrong based on 656 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)

Are You Up For the Challenge: 700 Level Questions

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
MBA Section Director V
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 7439
City: Pune
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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 54601 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 V
Joined: 02 Sep 2009
Posts: 61302
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

9
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 55406 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), respectively  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 61302
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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), respectively  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 61302
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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), respectively  [#permalink]

### Show Tags

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: 643
Location: India
GPA: 3.21
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 61302
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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: 174
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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: 492
GMAT 1: 630 Q49 V27
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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  S
Joined: 08 Dec 2015
Posts: 282
GMAT 1: 600 Q44 V27
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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 47150 times ]

Manager  S
Joined: 29 May 2016
Posts: 90
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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 S
Joined: 23 Jul 2015
Posts: 139
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

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  S
Joined: 12 Nov 2016
Posts: 684
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), respectively  [#permalink]

### Show Tags

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

### Show Tags

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
Senior Manager  G
Joined: 16 Feb 2015
Posts: 355
Location: United States
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

1
1
Bunuel 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)

Are You Up For the Challenge: 700 Level Questions

Explanantion: It’s a Section Formula problem (internal division case).

B (x’, y’) is such that

x’ = {mb+ na}/(m + n); y’ = {md + nc}/ (m + n).

In the given situation, a = 0, b = 3, c = -3, d = 3, m = 2 and n = 1.

we have x’ = (2 X 3 + 1 X 0)/3 = 2, and y’ = (2 X 3 + 1 X -3)/3 = 1,

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

IMO-C Please Give Kudos, If you find my explanation Good Enough Intern  B
Joined: 16 Jan 2020
Posts: 48
Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively  [#permalink]

### Show Tags

Just a little question.. how do you decide which one is m and which one is n. I took m/n as 1/2 and you took it as 2/1

Thank you!

Narenn wrote:
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 Re: The coordinates of points A and C are (0, -3) and (3, 3), respectively   [#permalink] 25 Jan 2020, 22:16
Display posts from previous: Sort by

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