Asked by Mike
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?
Answers
Answered by
Reiny
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
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.