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Question 1026800: A line is drawn from point A(-1, 2) to B(3, 4). Which point partitions the segment into the ratio 1:3? Also, which mathematical practices apply to this problem?
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! You may be able to solve this on your own. You will use Linear Equation for Two Given Points, and the Distance Formula. You are looking for two unknown points, (x,y).
(Concepts should become clear, but the algebra steps may take most of the work.)
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Form the equation of the line containing points A and B. Put the equation into slope-intercept form. This should be like the form y=mx+b. Any point on the line is like (x,mx+b).
The segment from A(-1,2) to B(3,4), you want to cut into three equal parts, and you want to find the two points, unknown, each of which cuts AB into  and  of the length of AB. This will require Distance Formula.
From A, one of these x values will be within AB and one of them will NOT be within AB:
That still needs you to find the equation for the line AB; and upon solving this equation for x, you need to decide which x value is the one you want. Then you would still not be finished.
.... because you also want to find the point one-third of the way FROM B TO A.
I still did not fully solve this problem (for you) myself yet. Maybe now you understand the method well enough that you can do the rest of the work.
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