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Question
Find the equation of a line which is equidistant from the lines x = − 2 and x = 6.
Solution
The lines x = − 2 and x = 6 pass through the points (−2, 0) and (6, 0), respectively. Let (h, k) be the mid-point of the line joining the points (−2, 0) and (6, 0).
\[\therefore \left( h, k \right) = \left( \frac{- 2 + 6}{2}, 0 \right) = \left( 2, 0 \right)\]
The given lines are parallel to the y-axis and the required line is equidistant from theses lines.
Hence, the required line is parallel to the y-axis, which is given by x = k.
This line passes through (2, 0).
∴ 2 = k
\[\Rightarrow\] k = 2
Hence, the equation of a line that is equidistant from the lines x = − 2 and x = 6 is x = 2.
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