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Sagot :
The statement "They are parallel and congruent" is true for the line segments.
Given that, triangle ABC is translated using the rule (x, y) → (x + 1, y − 4) to create triangle A′B′C′.
What is translation?
In mathematics, a translation is an up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another.
Now, let us consider coordinates as [tex]A(2,3)[/tex] and [tex]B(-4, 6)[/tex].
By using rule (x, y) → (x + 1, y − 4), we get [tex]A'[/tex] as (2+1, 3-4)=(3, -1) and [tex]B'[/tex] as (-4+1, 6-4)=(-3, 2).
Now, using the distance formula, [tex]Distance=\sqrt{(x_{2}-x_{1} )^{2} +(y_{2}-y_{1} )^{2} }[/tex] we have to calculate the distance of AA' and BB'.
That is, [tex]AA'=\sqrt{(3-2)^{2} +(-1-3)^{2} } =\sqrt{17}[/tex] units.
[tex]BB'=\sqrt{(-3-(-4))^{2}+(2-6)^{2} }= \sqrt{17}[/tex].
Since the length of AA' and BB' are the same they congruent.
Therefore, the statement "They are parallel and congruent" is true for the line segments.
To learn more about the translation visit:
https://brainly.com/question/11914505.
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