Question

Line m is mapped onto line n by a dilation centered at the origin with a scale factor of 2. The equation of line m is 3x−2y=63x-2y=63x−2y=6 . Find the equation for line n showing all work for full credit.

Answer 1

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Answer:

  3x -2y = 12

Step-by-step explanation:

The constant in the standard form equation for a line is proportional to the distance of the line from the origin. Dilation by a factor of 2 moves the line to twice its original distance from the origin. The equation of the new line will have the constant 2×6 = 12:

  3x -2y = 12

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Additional comment

The actual distance of line ax+by=c from the origin is ...

  d = |c|/√(a²+b²)

The distance from any point in the plane to the line is ...

  d = |ax +by -c|/√(a²+b²)

The previous equation is for the special case of (x, y) = (0, 0), the distance from the origin.