What is the equation of a set of points equidistant from the lines y 5 and x ndash 4 ........

Explanation:

A set of points equidistant from the given two lines should lie on the dotted line as indicated. You can think of it as the perpendicular bisector to the base of an isosceles triangle formed by (–4, 5) and the two points on x = –4 and y = 5.
Or, the set of points equidistant from two lines form the angle bisector of the angle formed at the point of intersection of the two lines. The angle between these two lines is 900. Importantly, the lines are parallel to the axes. So, thinking of the line that is the angle bisector of this angle should not be too difficult.
This dotted line is at an angle of 135^o with respect to the positive direction of x–axis and also passes through (–4, 5).
Slope = m = tan (135^o) = –1.
Therefore, the equation is given by (y – y₁) = m
(x – x₁) where (x₁, y₁) is (–4, 5).
(y – 5) = –(x + 4)
x + y = 1