Find the point on the y-axis that is equidistant from A(6, −1) and B(−2, 3).

1. 1 · Write what is given and what is to be found. Given: A(6, −1) and B(−2, 3). To find: a point P on the y-axis with PA = PB.
2. 2 · Write the formula or theorem. Distance formula: d = √[(x₂ − x₁)² + (y₂ − y₁)²]. A point on the y-axis is (0, y).
3. 3 · Square both sides. PA = PB, so PA² = PB²: (0 − 6)² + (y + 1)² = (0 + 2)² + (y − 3)²
4. 4 · Expand and simplify.
   • 36 + y² + 2y + 1 = 4 + y² − 6y + 9
   • 2y + 37 = −6y + 13
   • 8y = −24, so y = −3
5. 5 · Check and box the answer. PA² = 36 + 4 = 40 and PB² = 4 + 36 = 40. Answer: P(0, −3).

Scoring tip: Take P as (0, y) at the start and say why. The y² terms always cancel, so you get a simple linear equation.