Question

triangle rst and its image, triangle rst, are graphed on the coordinate grid below. which rotation, using the origin as the center of rotation, transformed rst to rst? a 90° clockwise rotation a 90° counterclockwise rotation a 45° counterclockwise rotation

Explanation:

Step1: Identify vertex coordinates

Original triangle vertices:
$R(1,0)$, $S(1,2)$, $T(4,4)$
Image triangle vertices:
$R'(0,-1)$, $S'(2,-1)$, $T'(4,-4)$

Step2: Apply rotation rules

Recall 90° clockwise rotation rule:
$(x,y)
ightarrow (y,-x)$
Test for $R(1,0)$: $(0,-1) = R'$
Test for $S(1,2)$: $(2,-1) = S'$
Test for $T(4,4)$: $(4,-4) = T'$

Step3: Verify no other rule fits

90° counterclockwise rule: $(x,y)
ightarrow(-y,x)$ fails (e.g., $R(1,0)
ightarrow(0,1)
eq R'$)
45° rotation rule does not match any vertex pairs.

Answer:

a 90° clockwise rotation