BTGmoderatorDC wrote: ↑

Sat Jun 06, 2020 10:21 pm

cgpq_img2.png

In the diagram above, coordinates are given for three of the vertices of quadrilateral ABCD. Does quadrilateral ABCD have an area greater than 30?

(1) Point B has an x-coordinate of 4
(2) Quadrilateral ABCD is a parallelogram

OA B

Source: Magoosh

Let's take each statement one by one.

(1) Point B has an x-coordinate of 4.

Area of quadrilateral ABCD
= Area of ∆ABC + Area of ∆ACD
= 1/2*y-coordinate*AC + 1/2*y-coordinate*AC
= 1/2*y-coordinate*8 + 1/2*4*8
= 4*y-coordinate + 16

Since we do not the value of the y-coordinate of point B, we can't get the answer. insufficient.

(2) Quadrilateral ABCD is a parallelogram.

Given that quadrilateral ABCD is a parallelogram, AD is parallel to BC and AB is parallel to CD; thus, we can get the value of the coordinates of point B, thereby the area of quadrilateral ABCD. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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