# Math

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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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