Question

2. Perform the following transformations on ABCD:R90°A(3,5), B(1,7) C(-2,4), D (2,-1).What are the vertices of A', B', C', and D'

Answer 1

$\begin{gathered} \text{The rotation of a point (x,y) by an angle of }\theta,\text{ is given by} \\ (x\cdot\cos (\theta)-y\cdot\sin (\theta),x\cdot\sin (\theta)+y\cdot\cos (\theta)) \\ \text{ In this particular excercise, }\theta=90º,\text{ and} \\ \cos (90º)=0 \\ \sin (90º)=1, \\ \\ \text{ Thus, the rotation of a point (x,y) by an angle of 90º is} \\ (-y,x) \end{gathered}$$\begin{gathered} \text{For our points} \\ A(3,5)\to A^{\prime}(-5,3)_{} \\ B(1,7)\to B^{\prime}(-7,1) \\ C(-2,4)\to C^{\prime}(-4,-2)_{} \\ D(2,-1)\to D^{\prime}(1,2) \end{gathered}$