document.write( "Question 189663: Distance from a Point to a Line
\n" ); document.write( "13.The equation of a circle with centre O(0,0)is x^2+y^2=10.The points P(1,3) and Q(-3,-1)are endpoints of chord PQ.Find the exact distance from the centre of the circle to the chord.\r
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Algebra.Com's Answer #142346 by Edwin McCravy(20054) $\"\"$ $\"About$

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Distance from a Point to a Line
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document.write( "The distance from the center to the chord is the\r\n" );
document.write( "perpendicular distance. So let's draw a line segment\r\n" );
document.write( "from the center perpendicular to the chord. Label the point\r\n" );
document.write( "where it intersects the chord R:\r\n" );
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document.write( "Drow OP and OQ:\r\n" );
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document.write( "OPQ is isosceles because its two legs \r\n" );
document.write( "OP and OQ are radii of the same circle and thus\r\n" );
document.write( "are equal.\r\n" );
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document.write( "Therefore the altitude OR is the perpendicular \r\n" );
document.write( "bisector of PQ.\r\n" );
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document.write( "Therefore R is the midpoint of PQ\r\n" );
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document.write( "We use the midpoint formula\r\n" );
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document.write( "The midpoint between (,) and (,) is given by\r\n" );
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document.write( "So the midpoint R between P(1,3) and Q(-3,-1) is\r\n" );
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document.write( "R(, )\r\n" );
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document.write( "R(, )\r\n" );
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document.write( "R(-1,1)\r\n" );
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document.write( "Now we use the distance formula to find the\r\n" );
document.write( "distance OR from O(0,0) to R(-1,1)\r\n" );
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document.write( "Distance formula:\r\n" );
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document.write( "Edwin

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