Question

one vertex of a triangle is located at (0, 5) on a coordinate grid. after a transformation, the vertex is located at (5, 0). which transformations could have taken place? choose two correct answers. options: ( r_{0, -90^circ} ), ( r_{0, 90^circ} ), ( r_{0, 180^circ} ), ( r_{0, -180^circ} ), ( r_{0, 270^circ} )

Explanation:

Step1: 90° rotation formula

\( (x,y)
ightarrow (-y,x) \)

Step2: Apply to (0,5) for 90°

\( (-5,0)
eq (5,0) \)

Step3: 270° rotation formula

\( (x,y)
ightarrow (y,-x) \)

Step4: Apply to (0,5) for 270°

\( (5,0) = (5,0) \)

Step5: -90° rotation is 270°

\( (5,0) = (5,0) \)

Step6: 180° rotation formula

\( (x,y)
ightarrow (-x,-y) \)

Step7: Apply to (0,5) for 180°

\( (0,-5)
eq (5,0) \)

Step8: -180° rotation is 180°

\( (0,-5)
eq (5,0) \)

Answer:

\( R_{0,270^\circ} \), \( R_{0,-90^\circ} \)