Question

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

Answer 1

$\text{A line which is equidistant from two other lines, must have the same slope.}\text{The slope of y = 10 and y = - 2 is 0, i.e. line parallel to x-axis.}\text{The required line is also parallel to y = 10 and y = - 2}\therefore m=0\text{Also, the required line will pass from the mid-point of the line joining (0, -2) and (0, 10)}\text{Coordinates of this point will be}(0,\frac{10-2}{2})=(0,\frac{8}{2})=(0,4)\therefore \text{The equation of the require line is :}y-4=0(x-x_1)\Rightarrow y=4$