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Question
Find the equation of a line equidistant from the lines y = 10 and y = − 2.
Solution
The lines y = 10 and y = −2 pass through the points (0, 10) and (0, −2), respectively. Let (h, k) be the mid-point of the line joining the points (0, 10) and (0, −2).
\[\therefore \left( h, k \right) = \left( 0, \frac{10 - 2}{2} \right) = \left( 0, 4 \right)\]
The given lines are parallel to the x-axis and the required line is equidistant from these lines.
Hence, the required line is parallel to the x-axis, which is given by y = k.
This line passes through (0, 4).
∴ 4 = k
\[\Rightarrow\] k = 4
Hence, the equation of a line that is equidistant from the lines y = 10 and y = − 2 is y = 4..
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