Question

write a rule to describe the transformation.

Explanation:

Step1: Identify original coordinates

Original points:
$S=(2,-1)$, $V=(1,-2)$, $T=(5,-3)$, $U=(2,-5)$

Step2: Identify transformed coordinates

Transformed points:
$S'=(2,1)$, $V'=(2,2)$, $T'=(-2,2)$, $U'=(2,5)$

Step3: Analyze x and y changes

For x-coordinate: $x' = -x + 4$
Check: For $S(2,-1)$: $-2 + 4 = 2 = S'_x$; For $T(5,-3)$: $-5 + 4 = -2 = T'_x$
For y-coordinate: $y' = -y$
Check: For $S(2,-1)$: $-(-1) = 1 = S'_y$; For $U(2,-5)$: $-(-5) = 5 = U'_y$

Step4: Combine into transformation rule

The rule maps each $(x,y)$ to $(-x+4, -y)$

Answer:

The transformation rule is $(x,y) \to (-x + 4, -y)$