anonymous
  • anonymous
Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
to find the shortest distance between two lines you hvae to take distance perpendicular that intersects both the lines.
anonymous
  • anonymous
perpendicular slope is the reciprocal of the slope of any equation
anonymous
  • anonymous
perp slope = - reciprocal slope of any equation

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anonymous
  • anonymous
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

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