PrateekDua wrote:
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In the rectangular coordinate system above, if OQ >= PQ, is the area of region OPQ less than 30?
(1) The coordinates of point P are (6,0)
(2) The coordinates of point Q are (3,8)
I'm happy to help.
Statement #1:
The coordinates of point P are (6,0)The base = 6, but the height could be anything, so the area could be anything. This statement, alone and by itself, is
not sufficient.
Statement #2:
The coordinates of point Q are (3,8)This is tricky. Segment OQ has some length --- we could find this length from the Pythagorean theorem (3^2 + 8^2, then take a square root), but the exact number is not important. The requirement OQ >= PQ allows for two cases --- let's look at them:
Case #1: Suppose OQ = PQ --- then this would be an isosceles triangle, and when PQ came down 8 vertical units from point Q, it would have to go over three horizontal units to (6, 0) --- base = 6, height = 8, area = 12
Case #2: Suppose OQ > PQ --- then PQ would have to be steeper, and come down the 8 vertical units while going fewer than 3 horizontal units to the right. This would make the base less than 6, so the area would be less than 12.
Either way, we have a definitive answer to the prompt. This statement, alone and by itself, is
sufficient.
Answer =
(B)Does this make sense?
Mike
I could not understand ur explanation for statement B.
Are we assuming here points O and P are fixed , and we moving point Q in order to consider scenario of OQ>PQ ??
and how can be assume point P to be fixed ?? O is fixed since it is origin