1. The problem asks for a point P on the y-axis equidistant from points A(-5, 5) and B(3, 7). 2. Since P lies on the y-axis, its x-coordinate is 0, so P = (0, y). 3. Calculate the distance from P to A using the distance formula: $$d(P,A) = \sqrt{(0+5)^2 + (y-5)^2} = \sqrt{25 + (y-5)^2}$$ 4. Calculate the distance from P to B: $$d(P,B) = \sqrt{(0-3)^2 + (y-7)^2} = \sqrt{9 + (y-7)^2}$$ 5. Since P is equidistant from A and B, set distances equal: $$\sqrt{25 + (y-5)^2} = \sqrt{9 + (y-7)^2}$$ 6. Square both sides to eliminate square roots: $$25 + (y-5)^2 = 9 + (y-7)^2$$ 7. Expand the squares: $$(y-5)^2 = y^2 - 10y + 25$$ $$(y-7)^2 = y^2 - 14y + 49$$ 8. Substitute back: $$25 + y^2 - 10y + 25 = 9 + y^2 - 14y + 49$$ 9. Simplify both sides: $$y^2 - 10y + 50 = y^2 - 14y + 58$$ 10. Subtract $y^2$ from both sides: $$-10y + 50 = -14y + 58$$ 11. Add $14y$ to both sides: $$4y + 50 = 58$$ 12. Subtract 50 from both sides: $$4y = 8$$ 13. Divide both sides by 4: $$y = 2$$ 14. The coordinates of P are: $$P = (0, 2)$$ Final answer: $$P = (0, 2)$$