Question 965226
Slope of line through ( 1,-2 ) and ( 3, 1 ):
{{{ ( 1 -(-2) ) / ( 3 - 1 ) = 3/2 }}}
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Slope of line through ( 2,y ) and ( 1, -2 ) :
{{{ ( y -(-2) ) / ( 2 - 1 ) = ( y + 2 )/1 }}}
{{{ ( y + 2 )/1 = y + 2 }}}
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If the 1st slope is {{{ m[1] }}} and the 2nd
slope is {{{ m[2] }}}, then to be perpendicular
to each other:
{{{ m[2] = -1/m[1] }}} , so I can say:
{{{ y + 2 = -( 1/(3/2) ) }}}
{{{ y + 2 = -2/3 }}}
{{{ y = -2/3 - 6/3 }}}
{{{ y = -8/3 }}}
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check answer:
{{{ m[2] =  ( y -(-2) ) / ( 2 - 1 ) }}}
{{{ m[2] = ( -8/3 -(-2) ) / 1 }}}
{{{ m[2] = ( -8/3 +6/3 ) / 1 }}}
{{{ m[2] = -2/3 }}}
OK