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What is the area of the triangle with points (2,4), (3,6), (5,2)?

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What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink]

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New post 27 Sep 2017, 01:41
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Difficulty:

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Question Stats:

53% (02:37) correct 47% (02:06) wrong based on 36 sessions

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[GMAT math practice question]

What is the area of the triangle with points (2,4), (3,6), (5,2)?

A. 4
B. 5
C. 6
D. 7
E. 8
[Reveal] Spoiler: OA

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What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink]

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New post 27 Sep 2017, 02:06
MathRevolution wrote:
[GMAT math practice question]

What is the area of the triangle with points (2,4), (3,6), (5,2)?

A. 4
B. 5
C. 6
D. 7
E. 8


Draw three points A(2,4), B(3,6) and C(5,2) like this

Attachment:
Untitled.png
Untitled.png [ 10.15 KiB | Viewed 326 times ]


In order to calculate the area of the triangle ABC, we need to calc it in indirect way.

Draw point D(5,4). We could easily calculate the area of triangle ACD and ABD.

\(S_{ACD}=\frac{1}{2}*3*2=3\)
\(S_{ABD}=\frac{1}{2}*3*2=3\)

So we have \(S_{ABDC}=S_{ACD}+S_{ABD}=3+3=6\)

We could calculate the area of triangle BCD easily. CD=2 and the distance from B to CD is 2.

\(S_{BCD}=\frac{1}{2}*2*2=2\).

Now \(S_{ABC}=S_{ABDC}-S_{BCD}=6-2=4\)..

Answer A
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Expert Post
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What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink]

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New post 29 Sep 2017, 01:27
=>

The area of the triangle with points (a,b), (c,d) and (e,f) is

1| a c e a |
2| b d f b |= (1/2)| ad-bc+cf-de+eb-af |


1| 2 3 5 2 |
2| 4 6 2 4 |= (1/2)| 12-12+6-30+20-4 |= 1/2∙8=4

Ans: A
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Re: What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink]

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New post 30 Sep 2017, 09:18
MathRevolution wrote:
[GMAT math practice question]

What is the area of the triangle with points (2,4), (3,6), (5,2)?

A. 4
B. 5
C. 6
D. 7
E. 8


Area of a triangle formed by 3 points (x1,y1), (x2,y2) and (x3,y3) is given by the following formula.

Area = \(\frac{|x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|}{2}\) ==> \(\frac{|2(6-2)+3(2-4)+5(4-6)|}{2}\) = 4

Hence A is the answer.
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Re: What is the area of the triangle with points (2,4), (3,6), (5,2)?   [#permalink] 30 Sep 2017, 09:18
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