Question

In the following graph we observe line segment AB being mapped by translation to line segment A'B'. A. In two or more sentences, explain what test you could perform to check the validity of this translation. B. Prove mathematically that the translation is valid using the test you mentioned above.

Answer 1

Answer:

(b)$AB=A'B'=\sqrt{13} units$

Step-by-step explanation:

Part A

When a line segment goes under translation, the pre-image and the image are have the same length.

Therefore, to check if A'B' is a valid translation of AB, we determine the length of both line segments and compare.

Part B

$A(-4,6) and B(-2,3)\\AB=\sqrt{(3-6)^2+(-2-(-4))^2}\\=\sqrt{(-3)^2+(-2+4)^2} \\=\sqrt{9+4}\\AB=\sqrt{13} units$

Similarly

$A'(3,9) and B'(5,6)\\AB=\sqrt{(6-9)^2+(5-3)^2}\\=\sqrt{(3)^2+(2)^2} \\=\sqrt{9+4}\\A'B'=\sqrt{13} units$

Since $AB=A'B'=\sqrt{13} units$, we can conclude that the translation of AB to A'B' is valid.