imagining this line between the two points, its gradient would be

so the gradient of the line we want would be

the midpoint of this line would be

so our line is

you can ofcourse just solve algebraicly,

youre errors came in in changing the right side to 0 and in the expansion of the squared terms

]]>distance (x, y) to (-4, 3) = distance (x, y) to (4, 2)

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sqrt( [(x) - (-4)]^2 + [(3) - (y)]^2 ) = sqrt( [(4) - (x)]^2 + [(2) - (y)]^2 )

(x + 4)^2 + (3 - y)^2 = (4 - x)^2 + (2 - y)^2

x^2 + 16x + 16 + 9 - 6y + y^2 = 16 - 8x + x^2 + 4 - 4y + y^2

16x + 16 + 9 - 6y = 16 - 8x + 4 - 4y

24x + 10y - 5 = 0

y = - 12/5x + 5/10

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