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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