In the Rectangular Coordinate System Above, if Point A (Not Shown) GMAT Problem Solving

Question: In the rectangular coordinate system above, if point A (not shown) is equidistant from points O and B and the area of triangle OAB is 16, which of the following are the possible coordinates of point A?

1. (-2, 6)
2. (0, 4)
3. (2, -6)
4. (2, 6)
5. (4, 0)

“In the rectangular coordinate system above, if point A (not shown) is equidistant from points O and B and the area of triangle OAB is 16, which of the following are the possible coordinates of point A?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

Look at the diagram above:

Since A is equidistant from points O and B, then it must be somewhere on the green line (perpendicular bisector of OB)

(2, -6) and (2, 6) are not on that line. If A is at (0, 4) or (4, 0) then the area is ½ * 4 * 4 = 8

Correct option: A

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