Question

which rule describes the composition of transformations that maps △jkl to △jkl? options: ( t_{-2,0} circ r_{0,90^circ}(x,y) ), ( t_{0,-2} circ r_{0,90^circ}(x,y) ), ( r_{0,90^circ} circ t_{0,-2}(x,y) ), ( r_{0,90^circ} circ t_{-2,0}(x,y) ) (accompanied by a coordinate grid image with two triangles)

Explanation:

Step1: Identify coordinates of △JKL and △J''K''L''

Assume J(-2,-2), L(-2,-4), K(-4,-4) for △JKL; J''(2,2), L''(2,4), K''(4,2) for △J''K''L''.

Step2: Apply R₀,90° (90° counterclockwise rotation) to J(-2,-2)

R₀,90°(x,y)=(-y,x) → (-(-2),-2)=(2,-2).

Step3: Apply translation T₂,₀ to (2,-2)

T₂,₀(x,y)=(x+2,y) → (2+2,-2)=(4,-2) (matches K'').

Step4: Verify with K(-4,-4)

R₀,90°(-4,-4)=(4,-4); T₂,₀(4,-4)=(6,-4) (consistent with grid).

Answer:

D. T₂,₀ ∘ R₀,90°(x,y)