SOLUTION: The point B(1,2) is one tenth of the way from the point A(-3,4) to the point P(x,y). Find x and y.

Algebra ->  Length-and-distance -> SOLUTION: The point B(1,2) is one tenth of the way from the point A(-3,4) to the point P(x,y). Find x and y.      Log On


   

Question 853220: The point B(1,2) is one tenth of the way from the point A(-3,4) to the point P(x,y). Find x and y.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
AB%2FAP=1%2F10. Finding the equation for line AB will give also the line AP, because we want point P to also be on the line.

LINE AB, AP:
m=%284-1%29%2F%28-3-2%29=-3%2F5;
Applying point-slope form, y-2=-%283%2F5%29%28x-1%29
y=-%283%2F5%29%28x-1%29%2B2
y=-%283%2F5%29x%2B3%2F5%2B2
y=-%283%2F5%29x%2B13%2F5.

A general point on line AB or AP or BP, is the variable point, ordered pair (x, -(3/5)x+13/5).

You can use the Distance Formula to complete the proportion shown at the top of this posting and it will be in ONE unknown variable, x. It may give two solutions, and one of them will be the answer you want and the other will not be the answer you want. You might like to try this process yourself, so I am not showing the rest of that process (yet).