Data Sufficiency

AAPL wrote:If the area of quadrilateral ABCD equal to the area of quadrilateral AECD?

(1) The coordinates of the points A, B, C, and D are (0, 5), (6, 0), (0, -3), and (-2, 0), respectively.
(2) The point E lines on the line x = 6.

The OA is C.

I'm not sure about this DS question, I tried as follows,

(1) gives us quadrilateral ABCD. Not sufficient

(2) Gives us x coordinate of point E. Not sufficient

On combining, if E is the same as B (6,0) then are is equal. Otherwise not as the points, A and C are not equidistant from B.

Not Sufficient.

I think the correct answer is E.

Can someone help, please? Thanks!

The correct answer is C.

Let's see how.

I suggest you plot all the five points A, B, C, D, and E on the coordinate plane.

We have to determine whether the area of quadrilateral ABCD equal to the area of quadrilateral AECD.

The area of quadrilateral ABCD = The area of triangle ACD + The area of triangle ABD ------- (1)

And

The area of quadrilateral AECD = The area of triangle ACD + The area of triangle AED ------- (2)

For (1) and (2) to be equal, the area of triangle ABD must be equal to the area of triangle AED.

We see that the point E lies on the line BE.

Since for triangle ABD and triangle AED, the base AD and the height (a perpendicular from AD to BE) are common, their area (1/2*Base*Height) would also be equal. Sufficient.


The correct answer: C

Hope this helps!

-Jay
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