Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.
+129839 Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.
There are several ways to do this...here's one
Let (0, 4) be a point on the first line
Then.......a line with a negative reciprocal slope going through this point will have the equation :
y = -x + 4........so......we can find the intersection of this line with y = x - 6....set both equations equal
-x + 4 = x - 6 add x, 6 to both sides
10 = 2x divide both sides by 2
5 = x
So...using -x + 4, the y value at intersection = -1.......
So...we just need to find the distance from (0,4) to ( 5, -1) =
√[ (5)^2 + (4 + 1)^2 ] = 5√2 ≈ 7.07 units
Here's a pic....AB is the distance with A = (0,4) and B = (5, -1)
