SOLUTION: Point P is located at (−2, 7) and point R is located at (1, 0). Find the y value for the point Q that is located two over three the distance from point P to point R.

Algebra ->  Length-and-distance -> SOLUTION: Point P is located at (−2, 7) and point R is located at (1, 0). Find the y value for the point Q that is located two over three the distance from point P to point R.      Log On


   

Question 838152: Point P is located at (−2, 7) and point R is located at (1, 0). Find the y value for the point Q that is located two over three the distance from point P to point R.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Slope-Intercept form for a line, y=mx+b.
m=%280-7%29%2F%281-%28-2%29%29=-7%2F3;
b=y-mx, using either point of the line:
b=7-%28-7%2F3%29%28-2%29=7-14%2F3=%2821-14%29%2F3=7%2F3.
Line equation is highlight_green%28y=-%287%2F3%29x%2B7%2F3%29

Find distance from P to R, using Distance Formula.
PR=sqrt%28%28-2-1%29%5E2%2B%287-0%29%5E2%29
sqrt%28%28-3%29%5E2%2B%287%29%5E2%29
sqrt%289%2B49%29
highlight_green%28PR=sqrt%2858%29%29

Any point (x,y) on the line for PR will be in the form, (x,-(7/3)x+7/3), the expression for y being that of the equation's expression for the line.

You want the point Q(x, -(7/3)x+7/3) so that

-
Simplify that and solve for x. Realize, that one value will be good and the other value will need to be rejected.