Question 1127185
M( 3,7 )
N( 11, -6 )
Point W is on the y-axis, so the point is
( 0, y )
The distance squared from M to W is:
{{{ ( 0 - 3 )^2 + ( y - 7 )^2 }}}
The distance squared from N to W is:
{{{ ( 0 - 11 )^2 + ( y -(-6) )^2 }}}
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Set the distances equal to each other
{{{ (-3)^2 + ( y - 7 )^2 = (-11)^2 + ( y + 6 )^2 }}}
{{{ ( y - 7 )^2 - ( y + 6 )^2 = (-11)^2 - (-3)^2 }}}
{{{ y^2 - 14y + 49 - y^2 - 12y - 36 = 121 - 9 }}}
{{{ -26y + 13 = 112 }}}
{{{ -26y = 99 }}}
{{{ y = -99/26 }}}
the point is:
( 0, -99/26 )
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check the math. you can plug result
back into equation