Answer:
The line segments AA' and BB' are parallel and congruent
Step-by-step explanation:
we know that
When the transformation is a translation, the figure does not change its shape or dimensions,
so
AA'=BB'=CC'
therefore
The line segments AA' and BB' are parallel and congruent
Translation involves moving a function away from its original position.
The statement that describes the line segments is:
Both lines would be parallel and congruent
The translation is given as:
[tex]\mathbf{(x,y) \to (x + 1, y - 4)}[/tex]
Translation is a rigid transformation.
This means that, the image and the pre-image would have the same measure.
So, when a line is drawn from A to A' and B to B'
Assume the coordinates of A and B are:
[tex]\mathbf{A = (2,3) }[/tex]
[tex]\mathbf{B = (-4,6) }[/tex]
Apply transformation
[tex]\mathbf{A' = (2 + 1, 3 - 4) = (3,-1)}[/tex]
[tex]\mathbf{'B = (-4 + 1, 6 - 4) = (-3,2)}[/tex]
The distance of lines AA' and BB' is calculated using:
[tex]\mathbf{d = \sqrt{(x_2 -x_2)^2 + (y_2 - y_1)^2 }}[/tex]
So, we have:
[tex]\mathbf{AA' = \sqrt{(2 -3)^2 + (3 - -1)^2 = \sqrt{17}}}[/tex]
[tex]\mathbf{BB' = \sqrt{(-4 --3)^2 + (6 -2)^2 = \sqrt{17}}}[/tex]
Notice that:
[tex]\mathbf{BB' = AA' = \sqrt{17}}}[/tex]
Because translation is a rigid transformation, then lines AA' and BB' would also be congruent
Read more about translations at:
https://brainly.com/question/12463306
