Answer:
3√2
Step-by-step explanation:
You want the distance between the parallel lines ...
Distance
On a graph, the lines are separated by 6 units vertically or horizontally. The slope of each is 1, so the slope of a perpendicular line will be -1.
One way to think of the distance between the lines is as the altitude of the right triangle with legs equal to the horizontal and vertical distances between the lines. That altitude is 6/√2 = 3√2.
The distance between the lines is 3√2 ≈ 4.24264.
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Additional comment
The distance from point (x, y) to line ax+by+c=0 is ...
d = |ax+by+c|/√(a²+b²)
If a point satisfies the equation x -y +2 = 0, then its distance from parallel line x -y -4 = 0 will be ...
|-2 -4|/√(1² +(-1)²) = 6/√2 = 3√2
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