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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: 51304
Point A in the xy-coordinate system is shown below. Given two other po  [#permalink]

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23 Aug 2018, 21:59
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:33) correct 26% (01:46) wrong based on 46 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 470 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, 22:08
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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Point A in the xy-coordinate system is shown below. Given two other po &nbs [#permalink] 23 Aug 2018, 22:08
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