To represent the set of points equidistant from the line y = 1 and the point (0, 3), you can use the distance formula between a point (x, y) and a given point (0, 3), and set it equal to the distance between the point (x, y) and the line y = 1. The distance formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's denote the coordinates of the point on the line y = 1 as (x, 1). The distance from (x, 1) to (0, 3) is:
√((x - 0)^2 + (1 - 3)^2) = √(x^2 + 4)
So, the equation representing the set of points equidistant from the line y = 1 and the point (0, 3) is:
√(x^2 + 4) = √((x - 0)^2 + (y - 3)^2)
Simplifying the equation, you get:
x^2 + 4 = x^2 + (y - 3)^2
Now, you can subtract x^2 from both sides:
4 = (y - 3)^2
Finally, take the square root of both sides:
2 = y - 3
Add 3 to both sides:
y = 5
So, the equation representing the set of points equidistant from the line y = 1 and the point (0, 3) is y = 5.