Question 146952
Your answer for A is not correct.
The vector AB should be able to lead you from A to B.
Look at it this way.
{{{x[A]+x[AB]=x[B]}}}
for the x component and
{{{y[A]+y[AB]=y[B]}}}
for the y component of the vector.
You can then re-arrange those equations and determine the x and y components of the vector AB.
{{{x[AB]=x[B]-x[A]}}}
and
{{{y[AB]=y[B]-y[A]}}}
Using the values from A.
{{{x[AB]=x[B]-x[A]}}}
{{{x[AB]=3-1}}}
{{{x[AB]=2}}}
{{{y[AB]=y[B]-y[A]}}}
{{{y[AB]=-7-2}}}
{{{y[AB]=-9}}}
[AB]=[2,-9]
If I start at (1,2) on the grid, I need to move 2 units to the right 
(positive x) and move 9 units down (negative y) to reach point (3,-7).
b) The method is the same, 
For the x component,
{{{x[AB]=x[B]-x[A]}}}
{{{x[AB]=2+3t-2}}}
{{{x[AB]=3t}}}
For the y component,
{{{y[AB]=y[B]-y[A]}}}
{{{y[AB]=3-4t-3}}}
{{{y[AB]=-4t}}}
[AB]=[3t,-4t]