We will have the following:
2)
A(0, 7) : <7, -3>
[tex]A^{\prime}(7,4)[/tex]
B(1, 3) : <7, -3>
[tex]B^{\prime}(8,0)[/tex]
C(-1, -4) : <7, -3>
[tex]C^{\prime}(6,-7)[/tex]
D(-5, 1) : <7, -3>
[tex]D^{\prime}(2,-2)[/tex]
3)
From the graph we will have the following:
a.
[tex](x,y)\to(x+7,y+5)[/tex]
b.
[tex]\langle7,5\rangle[/tex]
***Explanation***
For point 2, we will simply apply the vector to the corresponding coordinates, that is:
We have the coordinates:
[tex]A(a,b)[/tex]
and the vector:
[tex]\langle c,d\rangle[/tex]
So, in order to determine the final image we will have to follow the transformation rule:
[tex]A^{\prime}(a+c,b+d)[/tex]
*For point 3, we will simply count the number of units the image has moved to the left or rigth and that will be our transformation rule for the x-axis, and the number of units the image has moved up or down and that will be our transformation rule for the y-axis.
In the case of the problem, the images moved 7 units to the rigth (+7) and then moved 5 units up (+5), so the transformation rule in coordinate notation is given by:
[tex](x,y)\to(x+7,y+5)[/tex]
And in order to write it in vector notation, we simply write the units the images move:
[tex]\langle7,5\rangle[/tex]
