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

The translation of line AB to line A'B' is valid and the translation rule is (x,y) ⇒ (x - 7, y - 3)

How to validate the translation?

The graph that completes the question is added as an attachment

From the graph, we have:

A = (3,9) and B = (5,6)

A' = (-4,6) and B' = (-2,3)

Subtract the x and y coordinates of A' from A and B' from B.

So, we have:

AA' = (3 + 4, 9 - 6)

AA' = (7, 3)

BB' = (5 + 2, 6 - 3)

BB' = (7, 3)

See that:

AA' = BB' = (7, 3)

This means that the line AB is translated 7 units left and 3 units down

How to prove the translation mathematically

The translation above means:

(x,y) ⇒ (x - 7, y - 3)

Recall that:

A = (3,9) and B = (5,6)

So, we have:

A' = (3 - 7, 9 - 3)

A' = (-4, 6)

Also, we have:

B' = (5 - 7, 6 - 3)

B' = (-2, 3)

Hence, the translation is valid

Read more about translation at:

https://brainly.com/question/8959437

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