document.write( "Question 810421: Given the points A(3,1), B(6,y) and C(12,-2), find the value(s) of y for which AB is perpendicular to BC \n" ); document.write( "

Algebra.Com's Answer #488133 by josgarithmetic(39623) $\"\"$ $\"About$

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Slope for line AB is $\"%28y-1%29%2F%286-3%29=%28y-1%29%2F3\"$ .
\n" ); document.write( "The slope wanted for line BC is $\"-3%2F%28y-1%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "What we should know is that the product of two slopes must be -1.\r
\n" ); document.write( "\n" ); document.write( " $\"%28%28y-1%29%2F3%29%28-3%2F%28y-1%29%29=-1\"$ but this does not solve anything.
\n" ); document.write( "We still want an expression for slope of BC, which is $\"%28-2-y%29%2F%2812-6%29=-%282%2By%29%2F6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now use this in the \"-1\" equation.
\n" ); document.write( " $\"%28%28y-1%29%2F3%29%2A%28-%282%2By%29%2F6%29=-1\"$
\n" ); document.write( " $\"%28%28y-1%29%2F3%29%28%282%2By%29%2F6%29=1\"$
\n" ); document.write( " $\"%28y-1%29%28y%2B2%29%2F%2818%29=1\"$
\n" ); document.write( " $\"%28y-1%29%28y%2B2%29=18\"$
\n" ); document.write( " $\"y%5E2%2By-2=18\"$
\n" ); document.write( " $\"y%5E2%2By-20=0\"$ Fortunately, factorable.
\n" ); document.write( "(y+5)(y-4)=0\r
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\n" ); document.write( "\n" ); document.write( " $\"highlight%28y=-5%29\"$ or $\"highlight%28y=4%29\"$ \n" ); document.write( "

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