Question

Point G is located at (3, -1) and point H is located at (-2, 3). Find the point that is 2/3 the distance from point G to point H. (5 points)
Select one:
a. (0.33, -1.67)
b. (-0.33, 1.67)
c. (-0.5, -1)
d. (6.33, -2.67)

Answer 1

Go 2/3 the distance in x from G to H
and 2/3 the distance in y from G to H.
These are the new coordinates.

Answer 2

Parametrize the line from G to H as
f(t) =G + t (H - G)={3 - 5 t, -1 + 4 t} t between 0 and 1
Notice the
f[0)=G
f[1]= H
f(1/2)= Midpoint from G to H
You need
\[


f(2/3)=\left(-\frac{1}{3},\frac{5}{3}\right)=(-0.333333, 1.66667)

\]