SOLUTION: The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the co

Algebra ->  Length-and-distance -> SOLUTION: The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the co      Log On


   

Question 1046324: The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
Answer is (2, 1).
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
B is some point, (x,y). From there, use the DISTANCE FORMULA, and the equation of a LINE containing two given points.

AB=2BC
sqrt%28%28x-0%29%5E2%2B%28y-%28-3%29%29%5E2%29=2%2Asqrt%28%28x-3%29%5E2%2B%28y-3%29%5E2%29
sqrt%28x%5E2%2B%28y%2B3%29%5E2%29=2%2Asqrt%28%28x-3%29%5E2%2B%28y-3%29%5E2%29
x%5E2%2B%28y%2B3%29%5E2=4%28%28x-3%29%5E2%2B%28y-3%29%5E2%29
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Maybe using the equation of the line would be more convenient before carrying all those multiplications from that previous equation.

y=mx-3
m=%283-%28-3%29%29%2F%283-0%29
m=6%2F3
m=2
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y=2x-3--------Substitute for y in the equation which came from Distance Formula result.

x%5E2%2B%282x-3%2B3%29%5E2=4%28%28x-3%29%5E2%2B%282x-3-3%29%5E2%29
x%5E2%2B%282x%29%5E2=4%28%28x-3%29%5E2%2B%282x-6%29%5E2%29
5x%5E2=4%28%28x-3%29%5E2%2B2%5E2%28x-3%29%5E2%29-----see carefully how there is a factor of x-3 distributed in the right member.
5x%5E2=4%28x-3%29%5E2%281%2B4%29
5x%5E2=4%2A5%2A%28x-3%29%5E2------common factor 5 on both sides
x%5E2=4%28x-3%29%5E2
x%5E2=4%28x%5E2-6x%2B9%29
x%5E2=4x%5E2-24x%2B36
3x%5E2-24x%2B36=0
Divide both sides by 3.
x%5E2-8x%2B12=0
highlight%28%28x-6%29%28x-2%29=0%29
highlight_green%28system%28x=6%2Cor%2Cx=2%29%29------------------------------evaluate the corresponding y values. Use the linear equation for this. Choose the combination, or point which is BETWEEN points A and C.


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How to know that the line containing points A and C has y-intercept of -3?
The problem description clearly says so. This was given as point A.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?
Answer is (2, 1).
You already have the answer, so?

By the way, I got the same answer: Coordinate point (2, 1).

Show me what you've tried, if you've tried anything, and I will guide you to the solution.