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

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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)   (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.





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Maybe using the equation of the line would be more convenient before carrying all those multiplications from that previous equation.





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--------Substitute for y in the equation which came from Distance Formula result.



-----see carefully how there is a factor of x-3 distributed in the right member.

------common factor 5 on both sides




Divide both sides by 3.


------------------------------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)   (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. 

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