Find the equation of a line equidistant from the lines y = 10 and y = – 2.
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