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# In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0)

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Math Expert
Joined: 02 Sep 2009
Posts: 60687
In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0)  [#permalink]

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09 Dec 2019, 03:03
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:26) correct 29% (01:30) wrong based on 48 sessions

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In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0), and (6,0), respectively. What is the area of triangular region PQS?

A. 25
B. 30
C. 35
D. 42
E. 50

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Joined: 16 Feb 2015
Posts: 268
Location: United States
Concentration: Finance, Operations
Re: In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0)  [#permalink]

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09 Dec 2019, 03:10
Bunuel wrote:
In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0), and (6,0), respectively. What is the area of triangular region PQS?

A. 25
B. 30
C. 35
D. 42
E. 50

Explanation:
Below Is the Image Attached For Reference.

Area= |14(0-0)+1(0-10)+6(10-0)/2|
=|50/2|
=25

IMO-A
Attachments

Capture12345.PNG [ 28.41 KiB | Viewed 470 times ]

Intern
Joined: 30 Sep 2019
Posts: 14
In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0)  [#permalink]

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15 Jan 2020, 01:30
1
rajatchopra1994 wrote:
Bunuel wrote:
In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0), and (6,0), respectively. What is the area of triangular region PQS?

A. 25
B. 30
C. 35
D. 42
E. 50

Explanation:
Below Is the Image Attached For Reference.

Area= |14(0-0)+1(0-10)+6(10-0)/2|
=|50/2|
=25

IMO-A

I'd just like to add my 2 cents to the above solution by Rajat. I'm not a big believer in needing to know more formulas than required, the good ol' 1/2*base*height also works just fine here.
In the figure provided by Rajat, simply drop a perpendicular to the X axis from the point (14,10), the height of this perpendicular is the height of the triangle, 10 in this case. The base is the distance between the points (1,0) and (6,0) which is 5.
So Area = 1/2*5*10 = 25.
In cases where one of the sides of the triangle does not lie solely along the X or Y axes, I would simply extend the vertices of the relevant side to form a right angled triangle and employ the Pythagoras theorem to find the length of that side.
In the xy-plane, the points P, Q and S have coordinates (14,10), (1,0)   [#permalink] 15 Jan 2020, 01:30
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