document.write( "Question 305317: A straight line thrrough the origin meets the parallel lines 4x+2y=9 and 2x+y=-6 at points P and Q respectively. Then the point O divided the segment PQ in the ratio.. \n" ); document.write( "

Algebra.Com's Answer #218581 by toidayma(44) $\"\"$ $\"About$

You can put this solution on YOUR website!
It would be much easier if you graph it. No matter what the line through O is, according to Thales's principle, we always have: OP/OQ = OM/ON whereas OM is the the distance from O to the line 4x + 2y = 9 and ON is the distance from O to the other line. (Since the two lines are parallel, O,M and N are on a line.)
\n" ); document.write( "The distance between O(0,0) and line 4x + 2y -9 = 0 is: $\"OM+=+absolute%284%2A0+%2B+2%2A0+-+9%29%2Fsqrt%284%5E2+%2B+2%5E2%29+=+9%2Fsqrt%2820%29\"$
\n" ); document.write( "The distance between O(0,0) and line 2x + y + 6 = 0 is: $\"OM+=+absolute%282%2A0+%2B+1%2A0+%2B6%29%2Fsqrt%282%5E2+%2B+1%5E2%29+=+6%2Fsqrt%285%29\"$
\n" ); document.write( "Thus, OP/OQ = OM/ON = $\"%289%2Fsqrt%2820%29%29%2F%286%2Fsqrt%285%29%29=+3%2F4\"$ \n" ); document.write( "

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