Answer:
m = (8 1/2, 2 1/6)
Step-by-step explanation:
You want the point m that partitions xy in a 5:1 ratio, given x(1, -2) and y(10, 3).
The point M that partitions AB into the ratio m:n is given by ...
M = (mB +nA)/(m+n)
Using this formula for the given ratio and points, we have ...
m = (5y +1x)/(5+1)
m = (5(10, 3) +(1, -2))/6 = (50+1, 15-2)/6
m = (51/6, 13/6) = (8 1/2, 2 1/6)