Final answer:
The y-coordinate on the y-axis equidistant from points A(-2, 0) and B(-1, 4) is found by setting the distances from (0, y) to A and B equal and solving for y, which results in a coordinate of (0, 2).
Step-by-step explanation:
The y-coordinate of the point on the y-axis equidistant from points A(-2, 0) and B(-1, 4) can be found by setting the distance from the y-axis point, say (0, y), to both A and B equal.
Distance from (0, y) to A(-2, 0):
√((0 - (-2))^2 + (y - 0)^2) = √(4 + y^2)
Distance from (0, y) to B(-1, 4):
√((0 - (-1))^2 + (y - 4)^2) = √(1 + (y - 4)^2)
Set the distances equal:
√(4 + y^2) = √(1 + (y - 4)^2)
Square both sides:
4 + y^2 = 1 + (y - 4)^2
Expand and solve for y:
4 + y^2 = 1 + y^2 - 8y + 16
Cancel y^2 and simplify:
8y = 16 - 3
Divide by 8:
y = ⅓ = 2
The y-coordinate is therefore 2, which makes the answer (c) 2.