Explanation
The question asks whether the area of the triangle is
greater than 12. For the area of the triangle, we will most likely be looking
for a valid base-height pair. AC
would be a valid base, and in that case the x
coordinate of point B would give us the dimension of a valid height. Let's
turn to the data statements, evaluating them separately first, as always.
Statement (1) tells us the coordinates of point B. We have
the height of ABC, but not the base.
But one thing to keep in mind in coordinate geometry is that every point
location describes a right triangle. So here, we can actually find the area of
the little triangle defined by points A, B, and (0, -3). It has a valid
base/height pair of 3 and 4 so its area is 6. Moreover, since
, this sub-triangle is smaller than the other
triangle that is part of ABC, so the
area of that part is greater than 6. Therefore the area of ABC must be greater than 12. Statement (1) is sufficient.
Statement (2) is similar in that we have the base of ABC, but no height. Can we make a tricky
inference here as we did for Statement (1)? We cannot. Statement (1) gave us two
dimensions of information about the triangle, but there is only one dimension
of information in the point that lies on the y-axis. Point B could be close to the axis, making a small
triangle, or far out, making a large one. Statement (2) is insufficient.
The correct answer is (A).
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