Question

Attached.

Answer 1

do you know how to write the equation of a line using vectors?

Answer 2

Yeah. I got one point already.

Answer 3

I got (4.4, 5.2)

Answer 4

a "direction vector" from E to F is (F-E)

normalize this to unit length
v= (F-E)/|F-E|

now start at E and go in the direction v 3 units
E+3v
or E-3v

Answer 5

ya follo' ?

Answer 6

I think so.

Answer 7

So I'm not sure where to go from here though. I have vector (8, -6) and I scaled it by 3/10 to get my last point. But how do I get the second one?

Answer 8

F-E = (10,1) - (2,7)= (8,-6) that is the direction from E to F
its magnitude is sqrt(64+36)= sqrt(100)= 10
so the unit length vector is (8/10, -6/10) or (0.8, -0.6)
call this v= (0.8,-0.6)

if we start at E and add v to it, we move 1 unit toward F
if we add 3v, we move 3 units away from E (toward F)
this means
E+3v= (2,7) + 3(0.8, -0.6) = (2,7) + (2.4, -1.8) = (4.4, 5.2)

Answer 9

now go in the opposite direction, go to point E -3v

Answer 10

here is a picture