Understanding the Problem
To find the nearest point on the y-axis to the given point (-2, 5), we first recognize that any point on the y-axis can be represented as (0, y). Our goal is to determine the value of y that minimizes the distance from the point (-2, 5) to (0, y).
Distance Formula
The distance D between two points (x1, y1) and (x2, y2) is given by the formula:
D = √((x2 - x1)² + (y2 - y1)²)
For our specific points (-2, 5) and (0, y), the distance becomes:
D = √((0 - (-2))² + (y - 5)²)
D = √(2² + (y - 5)²)
D = √(4 + (y - 5)²)
Minimizing the Distance
To minimize D, we can instead minimize D² because the square root function is increasing. Thus, we focus on:
D² = 4 + (y - 5)²
To find the minimum value of (y - 5)², we note that this is minimized when y = 5.
Nearest Point on the Y-Axis
Thus, the nearest point on the y-axis to the point (-2, 5) is:
- (0, 5)
Conclusion
The point on the y-axis that is closest to (-2, 5) is:
- (0, 5)
This point maintains the same y-coordinate as the original point, ensuring it is the minimum distance away.

(-2,7), (-2,5), etc...