Question

Find the distance between the parallel lines m and n whose equations are
y = x + 4 and y = x - 6, respectively.

Answer 1

to find the shortest distance between two lines you hvae to take distance perpendicular that intersects both the lines.

Answer 2

perpendicular slope is the reciprocal of the slope of any equation

Answer 3

perp slope = - reciprocal slope of any equation

Answer 4

so let's say we take perpendicular slope of x + 4 line. slope = 1 so perp slope = -1/1 = -1.

so y = -x + b. now let's just simplify b = 0 .we can do this only because our two lines are parallel.

so if we take y = -x

next step is to find the intersection of y= -x and y = x- 6.

so -x = x - 6
-2x = -6
x = 3
so y = -3

so we get point (3, -3) as intersection point.

now point POI between -x and x +4
-x = x + 4
-2x = 4
x = -2
hence y = 2

so (-2,2) is another intersection point.

now find the distance between the two using the distance equation

d = sqrt [ (x-x1)^2 + (y - y1)^2 ] using the two intersection points