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

 It is currently 22 Oct 2019, 22:15

### 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

# Area of Triangle when coordinates of three vertices are given

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 17 Mar 2014
Posts: 429
Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

27 Jul 2017, 09:17
1
21
00:00

Difficulty:

35% (medium)

Question Stats:

77% (02:31) correct 23% (02:40) wrong based on 154 sessions

### HideShow timer Statistics

Hi Bunuel,

How to calculate area of triangle when coordinates of three vertices are given. For example, how to solve following question.

On the coordinate plane there are 3 points A(-1, 1), B(0, -2), and C(3, 4). What is the area of the triangle connecting the 3 points?

(A) 15/4
(B) 15/2
(C) 15
(D) 13/4
(E) 13/2

Regards,
Ammu
Senior SC Moderator
Joined: 22 May 2016
Posts: 3575
Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

27 Jul 2017, 11:22
5
ammuseeru wrote:
Hi Bunuel,

How to calculate area of triangle when coordinates of three vertices are given. For example, how to solve following question.

On the coordinate plane there are 3 points A(-1, 1), B(0, -2), and C(3, 4). What is the area of the triangle connecting the 3 points?

(A) 15/4
(B) 15/2
(C) 15
(D) 13/4
(E) 13/2

Regards,
Ammu

Attachment:

tri.area.grid.rectangle.jpg [ 37.89 KiB | Viewed 33996 times ]

Because this triangle has no vertical or horizontal leg, plot its three coordinates, connect them, then draw a rectangle around the triangle (see diagram).

Then find area of rectangle and subtract the areas of the three yellow triangles, whose areas are easy to find because they are right triangles (their legs are base and height).

1. (Area of rectangle) - (area of OTHER triangles) = area of THIS triangle

Area of rectangle = (L * W)
L = 6 (count on the graph, or subtract y-coordinates at points B and C)
W = 4 (count, or subtract x-coordinates at points A and B)

Rectangle area = 24

2. Find area of three triangles (yellow) ABX, BCY, and DXY (coordinates are in red - find base and height for each by counting or subtracting x- and then y-coordinates)

Area of triangle ABX = $$\frac{1}{2} b*h = \frac{(3*4)}{2}$$ = 6

Area of triangle BCY = $$\frac{(6 * 3)}{2}$$ = 9

Area of triangle DXY = $$\frac{(1*3)}{2} = \frac{3}{2}$$

Total area of yellow triangles = 6 + 9 + $$\frac{3}{2}$$ = $$\frac{33}{2}$$

3. (Rectangle area) - (total area of 3 yellow triangles) =
area of THIS triangle

24 - $$\frac{33}{2}$$ =

$$\frac{48}{2} - \frac{33}{2} = \frac{15}{2}$$

Hope it helps.
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3333
Location: India
GPA: 3.12
Re: Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

27 Jul 2017, 10:57
4
5
Given data
x1=-1,y1=1
x2=0,y2=-2
x3=3,y3=4

Given the vertices of the triangle
Area = $$\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y1 - y3x1)|$$

Substiuting these values,
Area = $$\frac{1}{2} * |2 + 6 + 7|$$ = $$\frac{1}{2} * |15| = \frac{15}{2}$$(Option B)
_________________
You've got what it takes, but it will take everything you've got
##### General Discussion
Manager
Joined: 01 Feb 2017
Posts: 243
Re: Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

12 Aug 2017, 03:00
2
1
In Triangle ABC, let's consider side BC as base.
Length of BC= √(6^2+3^2) = √45

Now, Let's assume AD as perpendicular to side BC.
Slope of line AD= negative reciprocal of Slope BC= -1/2

Now,
Equation of BC: y=2x-2 &

Therefore, Coordinates of point D [Calculated by equating equations of line AD to BC]= (+1, 0).

Hence, Area of Triangle ABC= 1/2xBCxAD = 1/2x√45x√5= 15/2

Ans B.
Manager
Status: Enjoying the Journey
Affiliations: ND
Joined: 26 Sep 2017
Posts: 114
Schools: Rotman '21
WE: Marketing (Consulting)
Re: Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

03 Nov 2017, 00:48
pushpitkc wrote:
Given data
x1=-1,y1=1
x2=0,y2=-2
x3=3,y3=4

Given the vertices of the triangle
Area = $$\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y1 - y3x1)|$$

Substiuting these values,
Area = $$\frac{1}{2} * |2 + 6 + 7|$$ = $$\frac{1}{2} * |15| = \frac{15}{2}$$(Option B)

Hi pushpitkc,

Can you elaborate more on your answer, I understood what you did, but is this a rule or something, can you highlight the rule please. Your answer is very efficient and I would like to know how to use it.

Thanks,
NDND
_________________
"it takes more time to fix a mistake than to avoid one"
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything

High achievement always takes place in the framework of high expectation Charles Kettering
If we chase perfection we can catch excellence Vince Lombardi

GMAT Club Live: 5 Principles for Fast Math: https://gmatclub.com/forum/gmat-club-live-5-principles-for-fast-math-251028.html#p1940045
The Best SC strategies - Amazing 4 videos by Veritas: https://gmatclub.com/forum/the-best-sc-strategies-amazing-4-videos-by-veritas-250377.html#p1934575
Director
Joined: 02 Sep 2016
Posts: 649
Re: Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

10 Nov 2017, 03:33
I don't know if this is the right approach, but I solved it like this.

(Using the figure genxer123's post)

I did not extend the rectangle this way. Using the distance between points formula, I found YX and YB i.e. root 10 and 5 respectively. As opposite sides of a rectangle are equal, I took the opposite sides as root 10 and 5.

Area of rectangle= root 10*5

Area of the other triangle in the rectangle= 1/2 *root 10*5

So the area of the triangle that we had to find= 2.5* root 10= approx 8..... So I chose B.
_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Senior Manager
Joined: 22 Feb 2018
Posts: 419
Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

20 Mar 2018, 10:24
1
NDND wrote:
pushpitkc wrote:
Given data
x1=-1,y1=1
x2=0,y2=-2
x3=3,y3=4

Given the vertices of the triangle
Area = $$\frac{1}{2} *| (x1y2 - y1x2) + (x2y3 - y2x3) + (x3y1 - y3x1)|$$

Substiuting these values,
Area = $$\frac{1}{2} * |2 + 6 + 7|$$ = $$\frac{1}{2} * |15| = \frac{15}{2}$$(Option B)

Hi pushpitkc,

Can you elaborate more on your answer, I understood what you did, but is this a rule or something, can you highlight the rule please. Your answer is very efficient and I would like to know how to use it.

Thanks,
NDND

NDND
The area of triangle with vertices(A,B,C) having following coordinates
Attachment:

triangle.png [ 3.16 KiB | Viewed 28536 times ]

A : $$x_{1},y_{1}$$
B : $$x_{2},y_{2}$$
C : $$x_{3},y_{3}$$

is given by
A = $$\frac{{|x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})|}}{2}$$

https://www.mathopenref.com/coordtrianglearea.html
_________________
Good, good Let the kudos flow through you
Non-Human User
Joined: 09 Sep 2013
Posts: 13411
Re: Area of Triangle when coordinates of three vertices are given  [#permalink]

### Show Tags

13 May 2019, 01:51
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: Area of Triangle when coordinates of three vertices are given   [#permalink] 13 May 2019, 01:51
Display posts from previous: Sort by