Question

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.

Answer 1

(x+1, y-1)

Because if you look at the corresponding points 1 is added to the x-value of the original point and 1 is subtracted from the y-value of the original point

Answer 2

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).