Question

Can anyone please help me in this assignment did not get it

Answer 1

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

This is a rotation of 180 clockwise, so:

`\begin{gathered} x^(\prime)=x\cos (180)+y\sin (180) \\ y^(\prime)=-x\sin (180)+y\cos (180) \\ x^(\prime)=-x \\ y^(\prime)=-y \\ \text{The rule is:} \\ (x,y)\to(-x,-y) \\ \text{Verify:} \\ \text{for example:} \\ E=(-1,3) \\ E^(\prime)=(1,-3) \\ (-1,3)\to(-x,-y)\to(1,-3) \end{gathered}`