Question 709653: The line X+Y= 4 divides the line joining the points (-1,1) and (5,7) in the ratio.?
please explain me in detail...
Answer by josgarithmetic(39630)   (Show Source):
You can put this solution on YOUR website! Two ways to think from what you say:
You need to state the problem exactly as you found it presented to you.
The way you presented the problem is not perfectly clear.
A possible and maybe good understanding of what you want could be this:
What is the ratio of the lengths of the segment from the intersection of the two lines to either of the given points? If that is what you meant, then the process can go like this:
The line X+Y=4 will intersect the line defined by (-1,1) and (5,7) at some particular point. We want to find the equation of the line that contains these two given points, and determine at what point this line intersects X+Y=4.
Next we want to use the distance formula to calculate the length from the intersection point of the two lines to both of the given points. Now, express the ratio of these two lengths.
I EXPLAINED the process according to what I believe you want. I did not actually solve the problem. As a quick check of the answer, you could change the given equation to  , graph it, plot the two given points and draw the line containing them, and then measure or count(?) the distances from the intersection to each point; and you have a ratio close-to what you would calculate through equations and symbols.
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