document.write( "Question 1165878: hey, i need help for this :) Find the point (𝑥,𝑦) on the line 𝑦=𝑥 that is equidistant from the points (6,8) and (8,0). Can you show me the steps too please, Thank you.
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Algebra.Com's Answer #790350 by KMST(5328)\"\" \"About 
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\n" ); document.write( "CONSIDERING DISTANCES:
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\n" ); document.write( "The square of the distance from a point (x,y) to the point (6,8) is
\n" ); document.write( "\"%28x-6%29%5E2%2B%28y-8%29%5E2\"
\n" ); document.write( "In the case the point has \"y=x\" ,
\n" ); document.write( "the square of that distance to (6,8) would be
\n" ); document.write( "\"%28x-6%29%5E2%2B%28x-8%29%5E2\" .
\n" ); document.write( "The square of the distance from a point (x,y) to the point (8,0) is
\n" ); document.write( "\"%28x-8%29%5E2%2B%28y-0%29%5E2\" , but if the point has \"y=x\" ,
\n" ); document.write( "the distance to (6,8) would be the square root of
\n" ); document.write( "\"%28x-8%29%5E2%2Bx%5E2\" .
\n" ); document.write( "If the point you are looking for is at the same distance from (6.8,qnd (8,0),
\n" ); document.write( "those distances are the same, and their squares are the same, so
\n" ); document.write( "\"%28x-6%29%5E2%2B%28x-8%29%5E2=%28x-8%29%5E2%2Bx%5E2\"
\n" ); document.write( "\"%28x-6%29%5E2%2Bcross%28%28x-8%29%5E2%29=cross%28%28x-8%29%5E2%29%2Bx%5E2\"
\n" ); document.write( "\"%28x-6%29%5E2=%2Bx%5E2\"
\n" ); document.write( "\"x%5E2-12x%2B36=x%5E2\"
\n" ); document.write( "\"cross%28x%5E2%29-12x%2B36=cross%28x%5E2%29\"
\n" ); document.write( "\"-12x%2B36=0\"
\n" ); document.write( "\"36=12x\"
\n" ); document.write( "\"36%2F12=x\"
\n" ); document.write( "\"highlight%28x=3%29\"
\n" ); document.write( "The point we are looking for is \"highlight%28C%283%2C3%29%29\"
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\n" ); document.write( "ANOTHER APPROACH:
\n" ); document.write( "The points equidistant from \"A%286%2C8%29\" and \"B%288%2C0%29\"
\n" ); document.write( "are on the bisector of segment AB.
\n" ); document.write( "That is the line perpendicular to AB through the midpoint of AB.
\n" ); document.write( "The midpoint of AB is \"M%28%286%2B8%29%2F2%2C%288%2B0%29%2F2%29=M%287.4%29\"
\n" ); document.write( "The slope of AB is \"%288-0%29%2F%286-8%29=8%2F%28-2%29=-4\"
\n" ); document.write( "The slope of a line perpendicular to AB is \"-%281%2F%28-4%29%29\"\"%22=%22\"\"1%2F4\"
\n" ); document.write( "The equation of the line going through \"M%287%2C4%29\" ,
\n" ); document.write( "with slope \"M=1%2F4\" is \"y-4=%281%2F4%29%28x-7%29\" ' The intersection of that line with \"y=x\" is the point that we look for.
\n" ); document.write( "Besides \"y=x\" , it must comply with \"y-4=%281%2F4%29%28x-7%29\" ,
\n" ); document.write( "so to find the value of \"x\" we solve \"x-4=%281%2F4%29%28x-7%29\" .
\n" ); document.write( "\"4%28x-4%29=4%2A%281%2F4%29%28x-7%29\"
\n" ); document.write( "\"4x-16=x-7\"
\n" ); document.write( "\"4x-x=-7%2B16\"
\n" ); document.write( "\"3x=9\"
\n" ); document.write( "\"x=9%2F3\" or \"highlight%28x=3%29\"
\n" ); document.write( "The point we are looking for is \"highlight%28C%283%2C3%29%29\"\r
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