Find a point on the line y = 4 that is equidistant from the two points (0,1) and (5,6)

The point on the line that is equidistant from points (0,1) and (5,6) is (2, 4).

Step-by-step explanation:

Let be , and . As we know that given function is a horizontal line, the condition of equidistance between that a point within that line and both points must be:

Where:

- Distance of point A with respect to P.

- Distance of point B with respect to P.

We expand this equivalence by Pythagorean Theorem:

And we get this expression:

If we know that , , , and , the expression is reduced to this:

The remaining component of the point within the line is:

The point on the line that is equidistant from points (0,1) and (5,6) is (2, 4).