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Points: (h, k) and (3h, -5k)

Slope: -3k/h

Perpendicular slope: h/3k

Midpoint: (2h, -2k)

Perpendicular equation: y--2k = h/3k(x-2h)

Multiply all terms by 3k: 3ky--6k2 = h(x-2h)

Equation in terms of 3ky = hx-2h2-6k2

Perpendicular bisector equation in its general form: hx-3ky-2h2-6k2 = 0

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