Answer:
The length of A'B' is 4 unit.
Step-by-step explanation:
Translation is a rigid transformation in which a figure or a line segment is shifted or moved without changing its shape and size,
That is, if the measurement of segment AB is 4 unit then after translation by any factor its measurement will not change,
So, the measurement of segment A'B' would be 4 unit.
Verification :
Let the coordinates of A and B are [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively,
Also, the rule of translation 1 unit right is,
[tex](x,y)\rightarrow (x+1, y)[/tex]
By the distance formula,
The measure of segment AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Thus, if A'B' is the transformed segment of segment AB,
Then, coordinates of A' and B' are [tex](x_1+1, y_1)[/tex] and [tex](x_2+1, y_2)[/tex]
So, the measure of segment A'B' = [tex]\sqrt{(x_2+1-x_1-1)^2+(y_2-y_1)^2}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, the measure of AB = measure of A'B'
