Final answer:
The point (0, b) on the y-axis that is equidistant from the points (2, 2) and (6, -5) is (0, -1), which is obtained by setting up an equation based on the distance formula and solving for b.
Step-by-step explanation:
To find the point (0, b) on the y-axis that is equidistant from the points (2, 2) and (6, −5), we can set up an equation based on the distance formula. For a point (x, y), the distance to (2, 2) is given by √[(x-2)^2 + (y-2)^2] and to (6, −5) by √[(x-6)^2 + (y+5)^2].
Since the point we are looking for is on the y-axis, x is 0, so these become √[(0-2)^2 + (b-2)^2] and √[(0-6)^2 + (b+5)^2], respectively. Setting these equal to each other, we get √[4 + (b-2)^2] = √[36 + (b+5)^2]. Squaring both sides to eliminate the square roots gives 4 + b^2 - 4b + 4 = 36 + b^2 + 10b + 25. Simplifying this, we find that b = -1, which is answer choice a).