Identify the translation rule on a coordinate plane that verifies that square A (-4, 3), B (-4, 8), C (-9, 3), D (-9, 8) and square A' (-3, 2), B' (-3, 7), C' (-8, 2), D' (-8, 7) are congruent.

Question

Mathematics

Jaylene Stevenson

24 July, 18:10

Identify the translation rule on a coordinate plane that verifies that square A (-4, 3), B (-4, 8), C (-9, 3), D (-9, 8) and square A' (-3, 2), B' (-3, 7), C' (-8, 2), D' (-8, 7) are congruent.

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Marcos Rose · Answer 1

Answer: The translation rule that verifies that square A (-4, 3), B (-4, 8), C (-9, 3), D (-9, 8) and square A' (-3, 2), B' (-3, 7), C' (-8, 2), D' (-8, 7) are congruent is

(x, y) ⇒ (x+1, y-1).

Step-by-step explanation: We are given to identify the translation rule on a coordinate plane that verifies that

square A (-4, 3), B (-4, 8), C (-9, 3), D (-9, 8) and square A' (-3, 2), B' (-3, 7), C' (-8, 2), D' (-8, 7) are congruent.

We see that the co-ordinates of the vertices of square ABCD and A'B'C'D' are related as follows:

A (-4, 3) ⇒ A' (-4+1, 3-1) = A' (-3, 2),

B (-4, 8) ⇒ B' (-4+1, 8-1) = B' (-3, 7),

C (-9, 3) ⇒ C' (-9+1, 3-1) = C' (-8, 2),

D (-9, 8) ⇒ D' (-9+1, 8-1) = C' (-8, 7).

Therefore, the required translation rule is given by

(x, y) ⇒ (x+1, y-1).

Thus, the translation rule that verifies that square A (-4, 3), B (-4, 8), C (-9, 3), D (-9, 8) and square A' (-3, 2), B' (-3, 7), C' (-8, 2), D' (-8, 7) are congruent is

(x, y) ⇒ (x+1, y-1).