document.write( "Question 1160834: Find the point on the line y=5x+1 that is closest to the point (3,5) . \n" ); document.write( "

Algebra.Com's Answer #784231 by Boreal(15235) $\"\"$ $\"About$

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$\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C5x%2B1%2C%28-1%2F5%29x%2B28%2F5%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Find the perpendicular line through (3, 5) that intersects the line y=5x+1
\n" ); document.write( "the perpendicular line has slope -(1/5), the negative reciprocal.
\n" ); document.write( "so y-y1=m(x-x1) point slope formula, m=slope and (x1, y1) the point.\r
\n" ); document.write( "\n" ); document.write( "y-5=(-1/5)(x-3)
\n" ); document.write( "y=(-1/5)x+3/5+5
\n" ); document.write( "y=(-1/5)x+(28/5)\r
\n" ); document.write( "\n" ); document.write( "Those two lines intersect at a point when (-1/5)x+(28/5)=5x+1
\n" ); document.write( "or (26/5)x=(23/5)
\n" ); document.write( "or x=(23/26)
\n" ); document.write( "when x=(23/26), y=141/26 using the 5x+1
\n" ); document.write( "and x=(23/26), y=-23/130+(728/130), or (705/130), which is 141/26\r
\n" ); document.write( "\n" ); document.write( "One could use the distance formula, but the perpendicular line to the intersection of the two will yield the closest point.
\n" ); document.write( "((-23/26), (141/26)) \n" ); document.write( "

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