Geometry

Find the distance between the lines with the equations

y = 3/2x+4 and −3x+2y = −1.

Round your answer to the nearest tenth.

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  1. y = 3/2x+4
    2y = 3x + 8
    3x - 2y + 8 = 0

    -3x + 2y = -1
    3x - 2y - 1 = 0 , so they are indeed parallel

    pick any point on the first line,
    e.g. let x = 2, then y = 7
    so (2,7) lies on the first

    distance from (2,7) to 3x - 2y - 1 = 0 is
    |2(3) - 2(7) -1|/√(3^2 + (-2)^2)
    = 9/√13
    = appr 2.5

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