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What is the ordinate (y-coordinate) of point C?

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What is the ordinate (y-coordinate) of point C?

by fskilnik@GMATH » Mon Mar 11, 2019 4:17 am

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GMATH practice exercise (Quant Class 20)

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Answer: [spoiler]_____(C)__[/spoiler]
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Source: — Data Sufficiency |
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by fskilnik@GMATH » Mon Mar 11, 2019 1:27 pm

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fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 20)

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[/size]
$$? = {y_C}$$

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$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{
\,OD = 2\sqrt 2 \hfill \cr
\Delta AOB\,\,{\rm{isosceles}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,\Delta ODB\,\,{\rm{isosceles}} \hfill \cr
\,BD = OD\,\,,\,\,OB = 4 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{
\,\Delta BEF\,\,{\rm{isosceles}} \hfill \cr
\,FG = GB = 4 - 3 \hfill \cr} \right.$$
$$\,\, \Rightarrow \,\,\,{\rm{line}}\,\,EC\,\,\,\left\{ \matrix{
\,{\rm{slope}} = 1\,\,\,\left( {{{45}^ \circ }} \right) \hfill \cr
\,F = \left( {2,0} \right) \in \,\,{\rm{line}} \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{line}}\,\,EC\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,C\,\,{\rm{unique}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.$$

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The correct answer is (C).

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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