Question

triangle qrs is transformed as shown on the graph. which rule describes the transformation? \\( r_{0, 90\degree} \\) \\( r_{0, 180\degree} \\) \\( r_{0, 270\degree} \\) \\( r_{0, 360\degree} \\)

Explanation:

Step1: Identify vertex coordinates

Original triangle QRS: $Q(2,-1)$, $R(4,-3)$, $S(3,1)$
Transformed triangle Q'R'S': $Q'(-1,-2)$, $R'(-3,-4)$, $S'(1,-3)$

Step2: Test 180° rotation rule

180° rotation about origin: $(x,y)\to(-x,-y)$
For $Q(2,-1)$: $(-2,1)$ does not match $Q'(-1,-2)$

Step3: Test 90° rotation rule

90° clockwise rotation: $(x,y)\to(y,-x)$
For $Q(2,-1)$: $(-1,-2)$ matches $Q'$
For $R(4,-3)$: $(-3,-4)$ matches $R'$
For $S(3,1)$: $(1,-3)$ matches $S'$
Note: $R_{0,270^\circ}$ (counterclockwise 270°) is equivalent to clockwise 90°, with rule $(x,y)\to(y,-x)$

Answer:

$R_{0, 270^\circ}$