document.write( "Question 924394: The abscissa of a point is two-fifths of its ordinate. Find the point if it is 5 units from (-2,2). \n" ); document.write( "

Algebra.Com's Answer #560810 by Fombitz(32388) $\"\"$ $\"About$

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Assume that the point is (x,y).
\n" ); document.write( "\"abscissa of a point is two-fifths of its ordinate\"
\n" ); document.write( " $\"x=%282%2F5%29y\"$
\n" ); document.write( "Then use the distance formula,
\n" ); document.write( " $\"%28x-%28-2%29%29%5E2%2B%28y-2%29%5E2=5%5E2\"$
\n" ); document.write( " $\"%28x%2B2%29%5E2%2B%28y-2%29%5E2=25\"$
\n" ); document.write( "Substituting,
\n" ); document.write( " $\"%28%282%2F5%29y%2B2%29%5E2%2B%28y-2%29%5E2=25\"$
\n" ); document.write( " $\"%284%2F25%29y%5E2%2B%288%2F5%29y%2B4%2By%5E2-4y%2B4=25\"$
\n" ); document.write( " $\"%2829%2F25%29y%5E2-%2812%2F5%29y%2B8=25\"$
\n" ); document.write( " $\"29y%5E2-60y%2B200=625\"$
\n" ); document.write( " $\"29y%5E2-60y-425=0\"$
\n" ); document.write( " $\"%28y-5%29%2829y%2B85%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"y-5=0\"$
\n" ); document.write( " $\"y=5\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"x=%282%2F5%295=2\"$
\n" ); document.write( "(2,5)
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\n" ); document.write( " $\"29y%2B85=0\"$
\n" ); document.write( " $\"29y=-85\"$
\n" ); document.write( " $\"y=-%2885%2F29%29\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"x=%282%2F5%29%28-%2885%2F29%29%29=-34%2F29\"$
\n" ); document.write( "(-34/29,-85/29)
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