eybrj2 wrote:

In the rectangular coordinate system above, if OP < PQ, is the area of region OPQ greater than 48 ?

(1) The coordinates of point P are (6,8)

(2) The coordinates of point Q are (13,0)

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\(?\,\,\,:\,\,\,{S_\Delta }\,\,\mathop > \limits^? \,\,48\)

\(\left( 1 \right)\,\,{S_\Delta }\,\,\mathop > \limits^{{\text{see}}\,\,{\text{our}}\,\,{\text{figure !}}} \,\,{S_{\Delta OPQ\,dash}} = \frac{{\left( {6 + 6} \right) \cdot 8}}{2} = 48\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle\)

\(\left( 2 \right)\,\,{\text{Geometric}}\,\,{\text{Bifurcation}}\)

Please note that:

> The first figure (on the right) is "the same" as the one we used in our first statement (see our figure), in which we answered <YES>

> The second figure (on the right-below) shows that the area-focus may be as small as we which (but still positive, of course) , hence <NO>

This solution follows the notations and rationale taught in the GMATH method.

Attachments

30Ago18_7q.gif [ 18.03 KiB | Viewed 44 times ]

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Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)

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