Question 978965
The slope of MN is:
{{{ ( 4 -(-2) ) / ( 0 -(-3) ) = ( 4 + 2 ) / 3 }}}
slope = {{{ 6/3 = 2 }}}
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The length of MN is:
{{{ sqrt( ( 0 -(-3) )^2 + ( 4 -(-2) )^2 ) }}}
{{{ sqrt( 3^2 + 6^2 ) }}}
{{{ sqrt( 9 + 36 ) = sqrt( 45 ) }}}
{{{ sqrt( 45 ) = 3*sqrt(5) }}}
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MN/2 = {{{ ( 3*sqrt(5) ) / 2 }}}
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x-coordinate of midpoint MN is:
{{{ ( 0 +(-3) ) / 2 = -3/2 }}}
y-coordinate of midpoint MN is:
{{{ ( 4 + (-2) ) / 2 = 2/2 }}}
{{{ 2/2 = 1 }}}
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The midpoint  of MN is at:
( -3/2, 1 ) 
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c) If N is the midpoint of segment MP, then P has coordinates (?, ?)
I know the length of MN is {{{ 3*sqrt(5) }}}
The length of NP must also = {{{ 3*sqrt(5) }}}
{{{ MN + NP = MP }}}
{{{ MP = 6*sqrt(5) }}}
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{{{ 6*sqrt(5) = sqrt( ( 0 - x )^2 + ( 4 - y )^2 ) }}}
{{{ 6*sqrt(5) = sqrt( x^2 + 16 - 8y + y^2 ) }}}
Square both sides
{{{ 36*5 = x^2 + 16 - 8y + y^2 }}}
{{{ x^2 + y^2 - 8y = 180 - 16 }}}
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The slope of MP is the same as MN, which is {{{ 2 }}}, so
{{{ 2 = ( y - 4 ) / ( x - 0 ) }}}
{{{ 2x = y - 4 }}}
{{{ y = 2x + 4 }}}
By substitutioon:
{{{ x^2 + ( 2x + 4 )^2 -8*( 2x + 4 ) = 164 }}}
{{{ x^2 + 4x^2 + 16x + 16 - 16x - 32 = 164 }}}
{{{ 5x^2 = 164 - 16 + 32 }}}
{{{ 5x^2 = 180 }}}
{{{ x^2 = 36 }}}
{{{ x = 6 }}}
and
{{{ y = 2x + 4 }}}
{{{ y = 2*6 + 4 }}}
{{{ y = 16 }}}
So,  point P has coordinates ( 6,16 )
Check:
Does the slope of MP = 2?
{{{ ( 16 - 4 ) / ( 6 - 0 ) = 2 }}}
{{{ 12/6 = 2 }}}
{{{ 2 = 2 }}}
OK
Hope all this helps
Here's a plot of the line going through M, N, and P
{{{ graph( 400, 400, -10, 10, -10, 20, 2x + 4 ) }}}