Question

The locus of a point that is equidistant from the lines `x + y - 2sqrt(2)` = 0 and `x + y - sqrt(2)` = 0 is ______.

Options

• `x + y - 5sqrt(2)` = 0

• `x + y - sqrt(2)` = 0

• `2x + 2y - 3sqrt(2)` = 0

• `2x + 2y - 5sqrt(2)` = 0

Answer 1

The locus of a point that is equidistant from the lines `x + y - 2sqrt(2)` = 0 and `x + y - sqrt(2)` = 0 is `underlinebb(2x + 2y - 3sqrt(2) = 0)`.

Explanation:

For any point P(x, y) that is equidistant from the given line, we have

`x + y - sqrt(2) = -(x + y - 2sqrt(2))`

or `2x + 2y - 3sqrt(2)` = 0.