Question

Coordinates of the image after a 180 degree clockwise rotation for A B C

Answer 1

A clockwise rotation is given by:

`\begin{gathered} x^(\prime)=x\cos (\theta)+y\sin (\theta) \\ y^(\prime)=-x\sin (\theta)+y\cos (\theta) \end{gathered}`

so:

`\begin{gathered} x^(\prime)=x\cos (180)+y\sin (180)=-x \\ y^(\prime)=-x\sin (\theta)+y\cos (\theta)=-y \end{gathered}`

Therefore:

`\begin{gathered} A(2,2)\to(-x,-y)\to A^(\prime)(-2,-2) \\ B(3,-2)\to(-x,-y)\to B^(\prime)(-3,2) \\ C(-1,3)\to(-x,-y)\to C^(\prime)(1,-3) \end{gathered}`