Question

1. parallelogram g h j k is transformed to create parallelogram ghjk. hadley thinks the transformation shown is a rotation 90° clockwise about the origin. hayden thinks the transformation shown is a rotation 270° counterclockwise about the origin. who is correct and why?

Explanation:

A rotation of \(90^{\circ}\) clockwise about the origin and a rotation of \(270^{\circ}\) counter - clockwise about the origin are equivalent transformations. When we rotate a point \((x,y)\) \(90^{\circ}\) clockwise about the origin, the transformation rule is \((x,y)\to(y, - x)\). When we rotate a point \((x,y)\) \(270^{\circ}\) counter - clockwise about the origin, the transformation rule is also \((x,y)\to(y,-x)\) (because \(270^{\circ}\) counter - clockwise \(=360^{\circ}-90^{\circ}\) clockwise). So both Hadley and Hayden are correct.

Answer:

Both Hadley and Hayden are correct. A \(90^{\circ}\) clockwise rotation about the origin and a \(270^{\circ}\) counter - clockwise rotation about the origin are equivalent transformations.