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 Your Progress

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.

Your resume gives the adcom a small but crucial window into who you are and how you may fit into their program. Make sure you make a stellar impression with the tips in this free guide!

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
02 Nov 2018, 16:13

1

This post received KUDOS

Expert's post

Sawant91 wrote:

Quantitative Section Test1 -> Question number 13

Image uploaded.

You have the base and height wrong. In a parallelogram shown in the figure below the base and height are marked. In this case, it would be a very long calculation to calculate the base and height from the given coordinates.

Attachment:

InkedCapture_LI.jpg [ 815.79 KiB | Viewed 3637 times ]

The problem is solved by calculating the area of the triangle ABD.

We can find area of triangle with Shoelace formula:

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
03 Nov 2018, 05:44

Thanks for your response.

I tried to solve by matrix method and got the answer is 7/2 for triangle BCD. I assumed the area of parallelogram is twice the triangle as there are two triangle present.

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
04 Nov 2018, 05:27

1

This post received KUDOS

Expert's post

Sawant91 wrote:

Thanks for your response.

I tried to solve by matrix method and got the answer is 7/2 for triangle BCD. I assumed the area of parallelogram is twice the triangle as there are two triangle present.

Is my understanding correct?

Yes, that is correct. Well done, it is a tough question.
_________________

Sandy If you found this post useful, please let me know by pressing the Kudos Button

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
18 Nov 2018, 20:56

2

This post received KUDOS

Expert's post

AE wrote:

Is there any other easy approach?

You may look at it this way.. 1) measure if diagonals a) C is (-7,7) so we are looking for hypotenuse with sides 7 each So \(\sqrt{7^2+7^2}=7√2\) b) diagonal BD Since B is (-3,4), D is mirror image from line AC which is x=y So D is (-4,3) Diagonal BD is hypotenuse with sides (-3-(-4) and (4-3) so 1 each.. Diagonal = \(\sqrt{1^2+1^2}=√2\)

Now area will be half of product of diagonals = 7√2*√2*1/2=7*2/2=7
_________________

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
22 Sep 2019, 05:10

sandy wrote:

Sawant91 wrote:

Quantitative Section Test1 -> Question number 13

Image uploaded.

You have the base and height wrong. In a parallelogram shown in the figure below the base and height are marked. In this case, it would be a very long calculation to calculate the base and height from the given coordinates.

Attachment:

InkedCapture_LI.jpg

The problem is solved by calculating the area of the triangle ABD.

We can find area of triangle with Shoelace formula:

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
22 Sep 2019, 09:23

3

This post received KUDOS

Asmakan wrote:

Hi Sandy, How we want to find the area of ABD and we are using the coordinate of C?

Hi, Unfortunately Sandy, is not with us

However, to answer your ques. - Simple trick don't complicate with formulas

Plz see the attach diag.

Let us extended the line from co-ordinate C to point M (-7,0) and to Point O (0,7) Extend the line from the co-ordinate B (-3,4) to Point O (0,7)

Extend the line from the co-ordinate D (4,-3) to Point M (-7,0) ( co-ordinate of point D = mirror image of the co-ordinate of Point B and hence the sign changes and value gets interchanged)

Now you can see 4 \(\triangle\) s

Since we need the Area of the parallelogram ABCD and that can be found = Area of the square AMCO - Sum of the Areas of all the 4 \triangle s

i.e. Area of the parallelogram ABCD = Area of the square AMCO - { Area of \(\triangle\) AMD + Area of \(\triangle\) DMC + Area of \(\triangle\) COB + Area of \(\triangle\) OAB }

First :

Area of the square \(AMCO = 7 * 7 = 49\) (distance between each point =7)

Now,

Area of \(\triangle\) AMD = \(\frac{1}{2} * 7 * 3\) = \(\frac{21}{2}\)( base =7 and height = distance from base to point D = 3)

Area of \(\triangle\) DMC = \(\frac{1}{2}* 7 * 3\) = \(\frac{21}{2}\)( base =7 and height = distance from base to point D = 3)

Area of \(\triangle\)COB = \(\frac{1}{2} * 7 * 3\) =\(\frac{21}{2}\)( base =7 and height = distance from base to point B = 3)

Area of \(\triangle\) OAB = \(\frac{1}{2} * 7 * 3\) =\(\frac{21}{2}\)( base =7 and height = distance from base to point B = 3)

Sum of all 4 \(\triangle\) s = \({4* \frac{21}{2}} = 42\)

Therefore Area of the parallelogram ABCD = 49 - 42 =7

Attachments

InkedCapture_LI.jpg [ 25.69 KiB | Viewed 2246 times ]

_________________

If you found this post useful, please let me know by pressing the Kudos Button

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
23 Dec 2019, 12:36

1

This post received KUDOS

pranab01 wrote:

Asmakan wrote:

Hi Sandy, How we want to find the area of ABD and we are using the coordinate of C?

Hi, Unfortunately Sandy, is not with us

However, to answer your ques. - Simple trick don't complicate with formulas

Plz see the attach diag.

Let us extended the line from co-ordinate C to point M (-7,0) and to Point O (0,7) Extend the line from the co-ordinate B (-3,4) to Point O (0,7)

Extend the line from the co-ordinate D (4,-3) to Point M (-7,0) ( co-ordinate of point D = mirror image of the co-ordinate of Point B and hence the sign changes and value gets interchanged)

it is the best approach. Thanks!

Now you can see 4 \(\triangle\) s

Since we need the Area of the parallelogram ABCD and that can be found = Area of the square AMCO - Sum of the Areas of all the 4 \triangle s

i.e. Area of the parallelogram ABCD = Area of the square AMCO - { Area of \(\triangle\) AMD + Area of \(\triangle\) DMC + Area of \(\triangle\) COB + Area of \(\triangle\) OAB }

First :

Area of the square \(AMCO = 7 * 7 = 49\) (distance between each point =7)

Now,

Area of \(\triangle\) AMD = \(\frac{1}{2} * 7 * 3\) = \(\frac{21}{2}\)( base =7 and height = distance from base to point D = 3)

Area of \(\triangle\) DMC = \(\frac{1}{2}* 7 * 3\) = \(\frac{21}{2}\)( base =7 and height = distance from base to point D = 3)

Area of \(\triangle\)COB = \(\frac{1}{2} * 7 * 3\) =\(\frac{21}{2}\)( base =7 and height = distance from base to point B = 3)

Area of \(\triangle\) OAB = \(\frac{1}{2} * 7 * 3\) =\(\frac{21}{2}\)( base =7 and height = distance from base to point B = 3)

Sum of all 4 \(\triangle\) s = \({4* \frac{21}{2}} = 42\)

Therefore Area of the parallelogram ABCD = 49 - 42 =7

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
22 Jul 2020, 00:47

Formula of Area of Parallelogram = 2 * Area of Triangle Formula of Area of Triangle when 2 coordinate points are given: |ad-bc| / 2 (a,b) = (-3,4) (c,d) = (-7,7)

Area of Triangle: (ad - bc) /2 = (-3*7) - (4*-7) / 2 = (-21 + 28) / 2 = 7/2 Area of Parallelogram = 2 * 7/2 = 7 Option C

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
22 Jul 2020, 18:48

Farina wrote:

Formula of Area of Parallelogram = 2 * Area of Triangle Formula of Area of Triangle when 2 coordinate points are given: |ad-bc| / 2 (a,b) = (-3,4) (c,d) = (-7,7)

Area of Triangle: (ad - bc) /2 = (-3*7) - (4*-7) / 2 = (-21 + 28) / 2 = 7/2 Area of Parallelogram = 2 * 7/2 = 7 Option C

Please correct me if I am wrong

Hi This approach is not correct,

when you mention "ad" - it doesn't mean = a * d, infact it is the distance from "a" to "d"

Here is an example from khan academy

Regards
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
22 Jul 2020, 23:40

1

This post received KUDOS

pranab223 wrote:

Farina wrote:

Formula of Area of Parallelogram = 2 * Area of Triangle Formula of Area of Triangle when 2 coordinate points are given: |ad-bc| / 2 (a,b) = (-3,4) (c,d) = (-7,7)

Area of Triangle: (ad - bc) /2 = (-3*7) - (4*-7) / 2 = (-21 + 28) / 2 = 7/2 Area of Parallelogram = 2 * 7/2 = 7 Option C

Please correct me if I am wrong

Hi This approach is not correct,

when you mention "ad" - it doesn't mean = a * d, infact it is the distance from "a" to "d"

Here is an example from khan academy

Regards

Thanks for correcting me. I saw this explanation which I have written on GREClub test explanations.
_________________

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
23 Jul 2020, 06:02

Farina wrote:

pranab223 wrote:

Farina wrote:

Formula of Area of Parallelogram = 2 * Area of Triangle Formula of Area of Triangle when 2 coordinate points are given: |ad-bc| / 2 (a,b) = (-3,4) (c,d) = (-7,7)

Area of Triangle: (ad - bc) /2 = (-3*7) - (4*-7) / 2 = (-21 + 28) / 2 = 7/2 Area of Parallelogram = 2 * 7/2 = 7 Option C

Please correct me if I am wrong

Hi This approach is not correct,

when you mention "ad" - it doesn't mean = a * d, infact it is the distance from "a" to "d"

Here is an example from khan academy

Regards

Thanks for correcting me. I saw this explanation which I have written on GREClub test explanations.

No worries,

Would you mind providing the question ID and question set of the GRECLUB test.

Regards
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
29 Jul 2020, 11:57

sandy wrote:

Sawant91 wrote:

Thanks for your response.

I tried to solve by matrix method and got the answer is 7/2 for triangle BCD. I assumed the area of parallelogram is twice the triangle as there are two triangle present.

Is my understanding correct?

Yes, that is correct. Well done, it is a tough question.

Hi, I tried solving this by finding the distance between the two points. For example, I first found the distance between point B and origin. Then point B and C. I was obviously wrong in this approach, but could you tell me how I was wrong here?

Re: If the coordinates of point B are (-3, 4) and the coordinate [#permalink]
29 Jul 2020, 12:09

Expert's post

ant99 wrote:

sandy wrote:

Sawant91 wrote:

Thanks for your response.

I tried to solve by matrix method and got the answer is 7/2 for triangle BCD. I assumed the area of parallelogram is twice the triangle as there are two triangle present.

Is my understanding correct?

Yes, that is correct. Well done, it is a tough question.

Hi, I tried solving this by finding the distance between the two points. For example, I first found the distance between point B and origin. Then point B and C. I was obviously wrong in this approach, but could you tell me how I was wrong here?

Please Sir,

read the explanations above. They go in depth
_________________