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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
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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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New post 09 Dec 2019, 03:03
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Question Stats:

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

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

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

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

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