Question

Segment AB is rotated to form A'B'¯¯¯¯¯¯¯.The coordinates of point A are (1, 5) and the coordinates of point B are (−6, 4).Which clockwise rotation around the origin results in the transformation of AB¯¯¯¯¯ to formA'B'¯¯¯¯¯¯¯? Select from the drop down arrow to choose the correct rotation.Rotation of 90Rotation of 180Rotation of 270

Answer 1

Rotation of 180

Step-by-step explanation

Step 1

Plot segment AB

let's check every option

Step 2

a) 90°

To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x)

so,let's check

`\begin{gathered} A(1,5)\Rightarrow90°\text{ rotatio}\Rightarrow A^(\prime)(5,-1 \\ B(-6,4)\Rightarrow rotation\text{ 90\degree}\Rightarrow B^(\prime)(4,-(-6))=B^(\prime)(4,6) \end{gathered}`

those are not the coordinates of A'B' hence we can discard the rotation of 90°

b)180 °

The rule for a rotation by 180° about the origin is (x,y)→(−x,−y)

so

`\begin{gathered} A(1,5)\Rightarrow90°\text{ rotatio}\Rightarrow A^(\prime)(-1,-5) \\ B(-6,4)\Rightarrow rotation\text{ 90\degree}\Rightarrow B^(\prime)(6,-4) \end{gathered}`

we can see that those are the coordinates of A'B'

hence

the answer is

Rotation of 180

I hope this helps you