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

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

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27 Sep 2017, 01:41
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Difficulty:

75% (hard)

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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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 [ 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 $$S_{ABC}=S_{ABDC}-S_{BCD}=6-2=4$$..

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Math Revolution GMAT Instructor
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Posts: 4120

Kudos [?]: 2885 [0], given: 0

GPA: 3.82
What is the area of the triangle with points (2,4), (3,6), (5,2)? [#permalink]

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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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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

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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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