Answer:
3.162 units
Explanation:
First identify the points that undergo transformation
You have;
A = (0,0) and B =(1,3)
The transformation is T: (x,y)= (x+2, y+1), this means to get the image you add the x coordinate of the object to 2, and the y coordinate to 1.
Finding coordinates of the image points A' and B'
A'= (0+2,0+1) = (2,1)
B'=(1+2, 3+1)=(3,4)
Finding the distance A'B'
The formula for distance d is

where
x₁=2
x₂=3
y₁=1
y₂=4
d=distance between two points
Applying the formula

The distance A'B' is √10 =3.162 units