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Points A and B are noted on the straight line y=2x+4.If the distance between them is 5,what is the difference between their y-coordinates?

  • Math -

    Consider a circle with centre A and B any point on the circle.
    let A be (0,4) , the y-intercept of y = 2x+4

    the B must be both on y = 2x+4 and the circle
    the equation of the circle would be
    x^2 + (y-4)^2 = 25
    sub in y = 2x+4
    x^2 + (2x+4 - 4)^2 = 25
    x^2 + 4x^2 = 25
    5x^2 = 25
    x^2 = 5
    x = ±√5

    consider x = +√5
    then y = 2√5 + 4

    and the difference in the y's between A and B is
    2√5+4 - 4 = 2√5

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