Question

2) Find the point, M, that is five-sixths of the distance from A(-7, 2) to B(-1, -4).

Answer 1

We have that
point A(-7,2)  and point B(-1,-4)

Step 1
find the distance AB
d=√[(-4-2)²+(-1+7)²]------------> √[36+36]
d=√72

step 2
find the point M
five-sixths of the distance from AB----------> (5/6)*√72

see the attached figure
AC/AB=x/((5/6)*AB)
6/(AB)=x/((5/6)*AB)--------> 6=6x/5
x=30/6-------> x=5

CB/AB=y/((5/6)*AB)
6/AB=y/((5/6)*AB)---------> 6=6y/5
y=30/6-------> y=5

therefore
the coordinate x of point M is
A(-7,2)
Mx=-7+5=-2

the coordinate y of point M is
A(-7,2)
My=2-5=-3

the point M is (-2,-3)