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?
“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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