First, we need to find the distance between points A and C. We can use the distance formula, which states that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
In this case, the x₁ and y₁ coordinates correspond to point A (0, 4) and the x₂ and y₂ coordinates correspond to point C (-3, 5). Plugging in these values, we get:
d = √[(-3 - 0)² + (5 - 4)²]
= √[9 + 1]
= √10
Now, we want to find point B, which is located one fourth of the distance from point A to point C. To do this, we can find the x-coordinate of B by taking one fourth of the distance between the x-coordinates of A and C.
The x-coordinate of A is 0 and the x-coordinate of C is -3. Subtracting these values and multiplying by one fourth, we get:
xB = (0 - (-3)) * 1/4
= 3 * 1/4
= 3/4
So, the x-coordinate for point B is 3/4.