Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 17 Dec 2007
Posts: 8

In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
19 Dec 2007, 12:00
1
This post received KUDOS
11
This post was BOOKMARKED
Question Stats:
75% (01:57) correct 25% (01:36) wrong based on 336 sessions
HideShow timer Statistics
In the rectangular coordinate system, what is the area of triangle PQR with points Q=(0,3) R=(7,4) P(4,0) A. 12.5 B. 14 C. 10 D. 16 E. 25 OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/intherecta ... 80659.html
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 07 Nov 2017, 10:58, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.



CEO
Joined: 21 Jan 2007
Posts: 2704
Location: New York City

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
19 Dec 2007, 12:38
mbsnyc wrote: In the rectangular coordinate system, what is the area of triangle PQR with points
Q=(0,3) R=(7,4) P(4,0)
a. 12.5 b. 14 c. 10 d. 16 e. 25
A
plot the points
make a square
subtract all the unnecessary triangles around the plotted triangle.
anyone know a faster way to do this?



CEO
Joined: 21 Jan 2007
Posts: 2704
Location: New York City

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
19 Dec 2007, 12:41
bmwhype2 wrote: mbsnyc wrote: In the rectangular coordinate system, what is the area of triangle PQR with points
Q=(0,3) R=(7,4) P(4,0)
a. 12.5 b. 14 c. 10 d. 16 e. 25 A plot the points make a square subtract all the unnecessary triangles around the plotted triangle. anyone know a faster way to do this?
use distance formula for each of the sides.
sides are 5 5 7
an isos rt triangle.
bh/2 = 5*5 / 2 = 12.5



Intern
Joined: 17 Dec 2007
Posts: 8

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
19 Dec 2007, 12:45
How did you know it was a right triangle and not just isc?



CEO
Joined: 17 Nov 2007
Posts: 3525
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
19 Dec 2007, 12:45
bmwhype2 wrote: plot the points subtract all the unnecessary triangles around the plotted triangle.
The same way
Attachments
t57324.gif [ 2.49 KiB  Viewed 4598 times ]



CEO
Joined: 21 Jan 2007
Posts: 2704
Location: New York City

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
19 Dec 2007, 12:53
mbsnyc wrote: How did you know it was a right triangle and not just isc?
you're right. its simply an isosceles triangle. we can infer the height is 7 but im not sure how to get the base.



CEO
Joined: 29 Mar 2007
Posts: 2517

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
19 Dec 2007, 14:00
mbsnyc wrote: In the rectangular coordinate system, what is the area of triangle PQR with points
Q=(0,3) R=(7,4) P(4,0)
a. 12.5 b. 14 c. 10 d. 16 e. 25
I get A.
Using the distance formula I get sides 5,5, 7
5*5/2=12.5



Manager
Joined: 21 Mar 2008
Posts: 225

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
05 May 2008, 18:57
2
This post received KUDOS
2
This post was BOOKMARKED
The area of a triangle with coordinates (x1,y1), (x2,y2), (x3,y3) is
1/2x1(y2y3)+x2(y3y1)+x3(y1y2)



Senior Manager
Joined: 06 Aug 2011
Posts: 380

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
14 Feb 2014, 11:03
can we do this by distance formula.. square root (x2x1)^2+(y2y1)^2 I did that by this formula.. M geting 5, 5 and square root 50 respectively of three sides... so 5*5/2=12.5 Ans A. is it rite? whats another aproach?
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



Intern
Status: Never Give up!!!
Joined: 03 Aug 2012
Posts: 49
Location: India
Concentration: Finance, General Management

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
15 Feb 2014, 01:05
sanjoo wrote: can we do this by distance formula..
square root (x2x1)^2+(y2y1)^2
I did that by this formula.. M geting 5, 5 and square root 50 respectively of three sides... so 5*5/2=12.5 Ans A.
is it rite? whats another aproach? Yes you can do it with this formula... simplest and fastest approach. There are other approaches mentioned in the posts but those involve more steps. Like plotting a trapezium finding its area and then subtracting two 345 rt angled triangles to get the desired area.



Senior Manager
Joined: 28 Apr 2012
Posts: 304
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31 GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
16 Feb 2014, 10:15
http://www.mathopenref.com/coordtrianglearea.html
_________________
"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well." ― Voltaire
Press Kudos, if I have helped. Thanks!



Intern
Joined: 02 Feb 2014
Posts: 7
Location: United States
Concentration: Healthcare, Entrepreneurship

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
09 Nov 2014, 22:50
1
This post received KUDOS
1
This post was BOOKMARKED
To figure out if it's a right triangle we should figure out if two of the sides are vertical to each other.
side 1 coordinates are 0,3 and 4,0 => slope = 3/4 side 2 coordinates are 4,0 and 7,4 => slope = 4/3
slope side1 / slope side2 = (3/4)/(4/3) = 1 sides are perpendicular to each other and the triangle is right.
Now you can calculate side1 = 5 side2 = 5 area = (side1 x side2) / 2 = 12.5



Director
Joined: 23 Jan 2013
Posts: 600

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
10 Nov 2014, 01:33
2
This post received KUDOS
1
This post was BOOKMARKED
we should count all three sides of PQR, so we get
5,5,5*sqrt2, meaning it is right triangle with 45, 45, 90 degree angles
so we only need to 5*5/2=12.5
A



Senior Manager
Joined: 17 Jun 2015
Posts: 252
GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
29 Dec 2015, 13:48
Adding to the diagram by walker, if once calculates the area of the triangle that has QR as the hypotenuse, it comes to be a noninteger, which subtracted from a whole integer (28) would give a non integer. The only non integer options is A
_________________
Fais de ta vie un rêve et d'un rêve une réalité



Math Expert
Joined: 02 Sep 2009
Posts: 44419

Re: In the rectangular coordinate system, what is the area of [#permalink]
Show Tags
07 Nov 2017, 10:59




Re: In the rectangular coordinate system, what is the area of
[#permalink]
07 Nov 2017, 10:59






