anonymous
  • anonymous
Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.
Mathematics
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anonymous
  • anonymous
Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.
Mathematics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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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