Question

The vertices of figure STUV have coordinates S(−2, 2) , T(2, 3) , U(1, −1) , and V(−3, −1) .

The vertices of figure S'T'U'V' have coordinates S′(2, −2), T′(6, −1) , U(5,  −5) , and V'(1,  −5) .

Which transformation of ​ figure STUV ​ produced ​ figure S'T'U'V' ​ ?

1) a reflection across the x-axis

2) a reflection across the y-axis

3) a translation 4 units left and 4 units up

4) a translation 4 units right and 4 units down

Answer 1

4.a translation 4 units right and 4 units down

Answer 2

Answer: The correct option is

(4) a translation 4 units right and 4 units down.

Step-by-step explanation: Given that the vertices of figure STUV have coordinates S(−2, 2) , T(2, 3) , U(1, −1) , and V(−3, −1) and the figure S'T'U'V' have coordinates S′(2, −2), T′(6, −1) , U'(5, −5) , and V'(1, −5) .

We are to select the correct transformations of figure STUV that produce the figure S'T'U'V'.

We can see that the vertices of figure STUV are changed according to the following common rule to form the vertices of figure S'T'U'V':

S(−2, 2) ⇒ S'(-2+4, 2-4) = S'(2, -2),

T(2, 3) ⇒ T'(2+4, 3-4) = T'(6, -1),

U(1, -1) ⇒ U'(1+4, -1-4) = U'(5, -5),

V(-3, -1) ⇒ V'(-3+4, -1-4) = V'(1, -5).

Therefore, the rule is a translation one and is written as

(x, y) ⇒ (x+4, y-4).

That is, a translation rule of 4 units right and 4 units down.

Option (4) is CORRECT.