A line which is equidistant from the lines y = 10 and y = – 2

To Find: The equation of the line

Formula used: The equation of line is [y – y₁ = m(x – x₁)]

Explanation: A line which is equidistant from, two other lines,

So, the slopes must be the same .

Therefore, The slope of line y = 10 and y = – 2 is 0, because lines are parallel to the x–axis.

Since, The required line will pass from the midpoint of the line joining (0, – 2) and (0, 10)

The Midpoint formula =

So, The coordinates of the point will be (0, 4)

Since The equation of the line is :

y – 4 = 0(x – 0)

y = 4

Hence, The equation of the line is y = 4