Distance between 2 plotted points

[Guest]

I have two plotted points on my graph P(2,3) and Q(8,-9).
creating line PQ.
I wish to find the cordinates of R and S so that R lies between P and S
and PR=RS=SQ.

I can find the midpoint by bisecting the line
but don't know how to find and graph the point 1/3 of the line.

I have the answer but do not know how to get there.

Thanks for any help!

Archer

 

[Gene]

R((P+(1/3)*(Q-P)) for x and y
S((P+(2/3)*(Q-P)) for x and y
For R:
R_x = 2+(8-2)/3 = 4
R_y = 3+(-9-3)/3 = -1
R(4,-1)

Or just divide the x distance by 3 and add that to the starting from x P(x,y). Same with y.
It's easier to do than explain :twisted:

 

[pka]

Gene gave one way, here is a second
Using parametric equations the line segment PQ is: x(t)=2+6t & y(t)=3−12t, 0≤t≤1.
Now when t=0 we get P and t=1 we get Q.
So R is when t=(1/3) and S when t=(2/3).