Point E (1,5), marked on the coordinate line, are located at the same distance from points B (-3) and F.

Point E (1,5), marked on the coordinate line, are located at the same distance from points B (-3) and F. Find the coordinate of point F. Calculate the distance between points D and F.

1) Let the point F have coordinate x. From the condition of the problem it is known that the point E (1,5), marked on the coordinate line, is located at the same distance from the points B (- 3) and F (x), which means that in order to find the coordinate of the point F, we find and equate the lengths of the segments BE and FE. BE = | 1.5 – (- 3) | = 4.5 and FE = | 1.5 – x |. We get the equation:

| 1.5 – x | = 4.5.

It has two solutions:

1.5 – x₁ = – 4.5;

x₁ = 4.5 + 1.5;

x₁ = 6 – coordinate of point F,

or 1.5 – x₂ = 4.5;

x₂ = 1.5 – 4.5;

x₂ = – 3 – does not satisfy the condition of the problem.

Answer: the coordinate of point F takes the value 6.

2) Let point D have coordinate y. If F (6), then the distance between points D and F will be: DF = | 6 – y |.

Answer: the distance between points D and F will be | 6 – y |.