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11 Mar 2019, 05:26
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C
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Difficulty:
85%
(hard)
Question Stats:
46% (02:15) correct
54%
(02:31)
wrong
based on 162
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GMATH practice exercise (Quant Class 20)
What is the ordinate (y-coordinate) of point C ?
(1) \(OD = 2\sqrt 2\)
(2) Triangle AOB is isosceles
What is the ordinate (y-coordinate) of point C ?
(1) \(OD = 2\sqrt 2\)
(2) Triangle AOB is isosceles
11 Mar 2019, 14:38
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fskilnik
\(? = {y_C}\)
\(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{\\
\,OD = 2\sqrt 2 \hfill \cr \\
\Delta AOB\,\,{\rm{isosceles}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{\\
\,\Delta ODB\,\,{\rm{isosceles}} \hfill \cr \\
\,BD = OD\,\,,\,\,OB = 4 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{\\
\,\Delta BEF\,\,{\rm{isosceles}} \hfill \cr \\
\,FG = GB = 4 - 3 \hfill \cr} \right.\)
\(\,\, \Rightarrow \,\,\,{\rm{line}}\,\,EC\,\,\,\left\{ \matrix{\\
\,{\rm{slope}} = 1\,\,\,\left( {{{45}^ \circ }} \right) \hfill \cr \\
\,F = \left( {2,0} \right) \in \,\,{\rm{line}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{line}}\,\,EC\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,C\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\)
The correct answer is (C).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
