Final answer:
The point on the y-axis equidistant from two given points (x₁, y₁) and (x₂, y₂) is found by averaging the y-coordinates of those points. The final coordinate is (0, M_y), where M_y = (y₁ + y₂) / 2.
Step-by-step explanation:
To find a point on the y-axis that is equidistant from the points (x₁, y₁) and (x₂, y₂), we can use the midpoint formula for the y-coordinates, since any point on the y-axis has an x-coordinate of 0. The midpoint of the y-coordinates of two points will yield the y-coordinate of the point on the y-axis that is equidistant from both points.
The midpoint formula for the y-coordinates is given by:
M_y = (y₁ + y₂) / 2
Applying this formula, we can find the y-coordinate (M_y) of the desired point on the y-axis:
M_y = (y₁ + y₂) / 2
Therefore, the point on the y-axis that is equidistant from (x₁, y₁) and (x₂, y₂) is (0, M_y).