Answer:
3.162 units
Step-by-step 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
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where
x₁=2
x₂=3
y₁=1
y₂=4
d=distance between two points
Applying the formula
[tex]d=\sqrt{(3-2)^2+(4-1)^2} \\\\\\d=\sqrt{1^2+3^2} \\\\\\d=\sqrt{1+9} \\\\\\d=\sqrt{10} \\\\\\d=3.162[/tex]
The distance A'B' is √10 =3.162 units
