Rotation of 180
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
[tex]\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}[/tex]
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
[tex]\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}[/tex]
we can see that those are the coordinates of A'B'
hence
the answer is
Rotation of 180
I hope this helps you
