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# Point A in the xy-coordinate system is shown below. Given two other po

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Math Expert
Joined: 02 Sep 2009
Posts: 55228
Point A in the xy-coordinate system is shown below. Given two other po  [#permalink]

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23 Aug 2018, 22:59
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Difficulty:

25% (medium)

Question Stats:

75% (01:51) correct 25% (02:20) wrong based on 69 sessions

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Point A in the xy-coordinate system is shown below. Given two other points B (4a, b) and C (2a, 5b), what is the area of triangle ABC in terms of a and b?

A. 7ab/2

B. 9ab/2

C. 15ab/2

D. 4ab

E. 6ab

Attachment:

GMAT_PS_Magoosh_24000.png [ 3 KiB | Viewed 795 times ]

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Point A in the xy-coordinate system is shown below. Given two other po  [#permalink]

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23 Aug 2018, 23:08
Bunuel wrote:

Point A in the xy-coordinate system is shown below. Given two other points B (4a, b) and C (2a, 5b), what is the area of triangle ABC in terms of a and b?

A. 7ab/2

B. 9ab/2

C. 15ab/2

D. 4ab

E. 6ab

Attachment:
GMAT_PS_Magoosh_24000.png

Co-ordinate of the vertices of the triangle ABC are A (a,b), B (4a, b) and C (2a, 5b).

We need base and height in order to determine area of a triangle.

Base=AB=4a-a=3a (Since y-position is constant)
height=5b-b=4b (Distance between point C and intersection point of height with base, since x-position remains constant ,we can substract the y-positions of the two points to get the height)

So, $$Area=\frac{1}{2}*3a*4b=6ab$$

Ans. (E)
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Re: Point A in the xy-coordinate system is shown below. Given two other po  [#permalink]

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19 Mar 2019, 20:47
Hi All,

We're told that Point A is in the xy-coordinate system as shown - and that two other points B (4a, b) and C (2a, 5b) are also in the system. We're asked for the AREA of triangle ABC in terms of a and b. This question can be approached in a couple of different ways, including by TESTing VALUES.

IF...
a = 1, b = 1, then the three co-ordinates are....
(1,1), (4, 1) and (2, 5)

This means that the 'base' of the triangle is 3 (it's the distance between (1,1) and (4,1) and the 'height' is 4 (it's the distance between (2,5) and the 'base'). Thus, the area of the triangle is...

Area = (1/2)(base)(height) = (1/2)(3)(4) = 6

Thus, we're looking for an answer that equals 6 when a=1 and b=1. There's only one answer that matches...

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Re: Point A in the xy-coordinate system is shown below. Given two other po   [#permalink] 19 Mar 2019, 20:47
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