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

1.	Find the equation of a line equidistant from the lines y = 10 and y = – 2.
Answer» 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 = \(\Big[\frac{x+x_1}{2},\frac{y+y_1}{2}\Big]\) So, The coordinates of the point will be \(\Big[0,\frac{10-2}{2}\Big]\) (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

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

Answer»

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 = \(\Big[\frac{x+x_1}{2},\frac{y+y_1}{2}\Big]\)

So, The coordinates of the point will be \(\Big[0,\frac{10-2}{2}\Big]\) (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